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The talk focuses on expander graphs in conjunction with the combined use of SDPs and eigenvalue techniques for approximating optimal solutions to combinatorial optimization problems. In the first part of the talk I will explain how to construct cost-effective, expanding networks by using 'local' sparsifiers of graphs that emerge as a solution to a semidefinite program. In the second part of the talk I will show that the Unique Games Conjecture is false when the underlying constraint graph is a (spectral) expander. Namely, I will present a polynomial-time algorithm for Unique Games on expanding instances that finds a good assignment when there exists one. ©2009 Microsoft Corporation. All rights reserved.

This article is from PLoS ONE , volume 9 . Abstract In this paper, a parametric method is introduced to solve fuzzy transportation problem. Considering that parameters of transportation problem have uncertainties, this paper develops a generalized fuzzy transportation problem with fuzzy supply, demand and cost. For simplicity, these parameters are assumed to be fuzzy trapezoidal numbers. Based on possibility theory and consistent with decision-makers' subjectiveness and practical requirements, the fuzzy transportation problem is transformed to a crisp linear transportation problem by defuzzifying fuzzy constraints and objectives with application of fractile and modality approach. Finally, a numerical example is provided to exemplify the application of fuzzy transportation programming and to verify the validity of the proposed methods.

This article is from PLoS ONE , volume 9 . Abstract In this paper, a parametric method is introduced to solve fuzzy transportation problem. Considering that parameters of transportation problem have uncertainties, this paper develops a generalized fuzzy transportation problem with fuzzy supply, demand and cost. For simplicity, these parameters are assumed to be fuzzy trapezoidal numbers. Based on possibility theory and consistent with decision-makers' subjectiveness and practical requirements, the fuzzy transportation problem is transformed to a crisp linear transportation problem by defuzzifying fuzzy constraints and objectives with application of fractile and modality approach. Finally, a numerical example is provided to exemplify the application of fuzzy transportation programming and to verify the validity of the proposed methods.

Journal of Optimization Theory and Applications 1985: Volume 47 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1985-08_46_4 . Next issue: sim_journal-of-optimization-theory-and-applications_1985-09_47_1 .

A working theory of two-component two-phase (gas-liquid) nozzles, developed as part of Phase I, was used to conduct parametric performance analyses over a wide range of flow conditions and for varied fluid properties. Droplet breakup and the interface transport of momentum and thermal energy were considered in the analyses, but mass transfer and wall friction losses were excluded. Results from the parametric analyses compare favorably with experimental data and other theoretical analyses available in the literature. The sensitivity of the predicted nozzle performance to the assumptions concerning the droplet characteristics was examined, and criteria were developed for optimum nozzle designs based on the parametric analyses. A simplified procedure was developed for the quick estimation of the major dimensions for two-phase nozzles. Finally, the work extraction potential of two-phase nozzles was examined in terms of their performance criteria and system integration characteristics.

In this project of Information-theory and Optimization of Networked Systems (IONS), we developed the approaches of geometric programming, information-control duality, erasure information, and stochastic network optimization for communication networks. Pathfinder applications to missile defense, telecommunications, and biological networks are studied. Several major awards were received by the team of co-PIs, including Shannon Award, IEEE Hamming Medal, Presidential Early Career Award for Scientists and Engineers, and Technology Review TR35 Young Innovator Award.

In this project of Information-theory and Optimization of Networked Systems (IONS), we developed the approaches of geometric programming, information-control duality, erasure information, and stochastic network optimization for communication networks. Pathfinder applications to missile defense, telecommunications, and biological networks are studied. Several major awards were received by the team of co-PIs, including Shannon Award, IEEE Hamming Medal, Presidential Early Career Award for Scientists and Engineers, and Technology Review TR35 Young Innovator Award.

Journal of Optimization Theory and Applications 1978: Volume 25 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1978_25_index . Next issue: sim_journal-of-optimization-theory-and-applications_1978-05_25_1 .

Journal of Optimization Theory and Applications 1978: Volume 25 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1978_25_index . Next issue: sim_journal-of-optimization-theory-and-applications_1978-05_25_1 .

Journal of Optimization Theory and Applications 1973: Volume 11 , Issue Index. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1972-12_10_6 . Next issue: sim_journal-of-optimization-theory-and-applications_1973-01_11_1 .

Journal of Optimization Theory and Applications 2002: Volume 112 , Issue Contents. Digitized from IA1534532-02 . Previous issue: sim_journal-of-optimization-theory-and-applications_2001-12_111_3 . Next issue: sim_journal-of-optimization-theory-and-applications_2002-01_112_1 .

A working theory of two-component two-phase (gas-liquid) nozzles, developed as part of Phase I, was used to conduct parametric performance analyses over a wide range of flow conditions and for varied fluid properties. Droplet breakup and the interface transport of momentum and thermal energy were considered in the analyses, but mass transfer and wall friction losses were excluded. Results from the parametric analyses compare favorably with experimental data and other theoretical analyses available in the literature. The sensitivity of the predicted nozzle performance to the assumptions concerning the droplet characteristics was examined, and criteria were developed for optimum nozzle designs based on the parametric analyses. A simplified procedure was developed for the quick estimation of the major dimensions for two-phase nozzles. Finally, the work extraction potential of two-phase nozzles was examined in terms of their performance criteria and system integration characteristics.

Discrete manufacturing process design optimization (DMPDO) is a problem of significant importance and interest to the Air Force. Moreover, the complexity of parts that must be manufactured for airplane engines and other units makes this problem extremely difficult. This report summarizes the research that has been conducted in developing the generalized hill climbing (GHC) algorithm framework for discrete optimization problems in general, and the DMPDO problems in particular. Convergence conditions for GHC algorithms have been developed. Ordinal hill climbing (OHC) algorithms were introduced to exploit the efficiency of ordinal optimization and the effectiveness of GHC algorithms to obtain a new class of discrete optimization problem algorithms. The relationship between OHC algorithms and genetic algorithms was also studied. Multiple sequence optimization using GHC algorithms were introduced to optimize across sets of DMPDO sequences. Simultaneous GHC algorithms were introduced as a generalization to optimize across a set of related discrete optimization problems. On-going interactions with researchers at the Materials Process Design Branch of the AFRL at WPAFB and at Austral Engineering and Software, Inc. has resulted in these algorithms being transitioned for application into commercial software tools designed to solve various DMPDO problems of interest to the Air Force.

The linear programming (LP) is one of the most popular necessary optimization tool used for data analytics as well as in various scientific fields. However, the current state-of-art algorithms suffer from scalability issues when processing Big Data. For example, the commercial optimization software IBM CPLEX cannot handle an LP with more than hundreds of thousands variables or constraints. Existing algorithms are fundamentally hard to scale because they are inevitably too complex to parallelize. To address the issue, we study the possibility of using the Belief Propagation (BP) algorithm as an LP solver. BP has shown remarkable performances on various machine learning tasks and it naturally lends itself to fast parallel implementations. Despite this, very little work has been done in this area. In particular, while it is generally believed that BP implicitly solves an optimization problem, it is not well understood under what conditions the solution to a BP converges to that of a corresponding LP formulation. Our efforts consist of two main parts. First, we perform a theoretic study and establish the conditions in which BP can solve LP [1,2]. Although there has been several works studying the relation between BP and LP for certain instances, our work provides a generic condition unifying all prior works for generic LP. Second, utilizing our theoretical results, we develop a practical BP-based parallel algorithms for solving generic LPs, and it shows 71x speed up while sacrificing only 0.1 accuracy compared to the state-of-art exact algorithm. As a result of the study, the PIs have published two conference papers and two follow-up journal papers are under submission. We refer the readers to our published work for details.

A working theory of two-component two-phase (gas-liquid) nozzles, developed as part of Phase I, was used to conduct parametric performance analyses over a wide range of flow conditions and for varied fluid properties. Droplet breakup and the interface transport of momentum and thermal energy were considered in the analyses, but mass transfer and wall friction losses were excluded. Results from the parametric analyses compare favorably with experimental data and other theoretical analyses available in the literature. The sensitivity of the predicted nozzle performance to the assumptions concerning the droplet characteristics was examined, and criteria were developed for optimum nozzle designs based on the parametric analyses. A simplified procedure was developed for the quick estimation of the major dimensions for two-phase nozzles. Finally, the work extraction potential of two-phase nozzles was examined in terms of their performance criteria and system integration characteristics.

Journal of Optimization Theory and Applications 1976: Volume 18 , Issue Index. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1975-12_17_5-6 . Next issue: sim_journal-of-optimization-theory-and-applications_1976-01_18_1 .

Journal of Optimization Theory and Applications 1999: Volume 103 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1999-09_102_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1999-10_103_1 .

Journal of Optimization Theory and Applications 1999: Volume 103 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1999-09_102_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1999-10_103_1 .

Journal of Optimization Theory and Applications 1999: Volume 103 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1999-09_102_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1999-10_103_1 .

Journal of Optimization Theory and Applications 1999: Volume 103 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1999-09_102_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1999-10_103_1 .

Journal of Optimization Theory and Applications 1999: Volume 103 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1999-09_102_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1999-10_103_1 .

The method of Lagrange for finding extrema of functions subject to equality constraints was published in 1788 in the famous book Mecanique Analytique. The works of Karush, John, Kuhn and Tucker concerning optimization subject to inequality constraints appeared more than 150 years after that. The purpose of this paper is to call attention to important papers, published as contributions to mechanics, containing fundamental ideas concerning optimization theory. The most important works in this respect were done primarily by Fourier, Cournot, Farkas and further by Gauss, Ostrogradsky and Hamel. (Author)

Bibliography: leaf 15

The broad research objective of this project was the development of optimization algorithms and related system-theoretic aspects for the integrated design of flexible structures and their control systems, and shape design.

Journal of Optimization Theory and Applications is an active publication that covers all aspects of mathematical optimization techniques and their applications in science and engineering. It was established in 1967 and is published monthly by Springer New York LLC. The aim of the journal is to provide a platform for researchers and practitioners to share their innovative work and discoveries in the field of mathematical optimization. It features original research papers, review articles, and case studies that cover a wide range of topics, including linear programming, nonlinear programming, convex optimization, stochastic optimization, and global optimization. Journal of Optimization Theory and Applications can be found online at: https://www.springer.com/journal/10957

Journal of Optimization Theory and Applications is an active publication that covers all aspects of mathematical optimization techniques and their applications in science and engineering. It was established in 1967 and is published monthly by Springer New York LLC. The aim of the journal is to provide a platform for researchers and practitioners to share their innovative work and discoveries in the field of mathematical optimization. It features original research papers, review articles, and case studies that cover a wide range of topics, including linear programming, nonlinear programming, convex optimization, stochastic optimization, and global optimization. Journal of Optimization Theory and Applications can be found online at: https://www.springer.com/journal/10957

Journal of Optimization Theory and Applications is an active publication that covers all aspects of mathematical optimization techniques and their applications in science and engineering. It was established in 1967 and is published monthly by Springer New York LLC. The aim of the journal is to provide a platform for researchers and practitioners to share their innovative work and discoveries in the field of mathematical optimization. It features original research papers, review articles, and case studies that cover a wide range of topics, including linear programming, nonlinear programming, convex optimization, stochastic optimization, and global optimization. Journal of Optimization Theory and Applications can be found online at: https://www.springer.com/journal/10957

Physical quantities in QCD are independent of renormalization scheme (RS), but that exact invariance is spoiled by truncations of the perturbation series. "Optimization" corresponds to making the perturbative approximant, at any given order, locally invariant under small RS changes. A solution of the resulting optimization equations is presented. It allows an efficient algorithm for finding the optimized result. Example results for R(e+e-)=3(Sum q_i^2)(1+R) to fourth order (NNNLO) are given that show nice convergence, even down to arbitrarily low energies. The Q=0 "freezing" behaviour, R=0.3+/-0.3, found at third order is confirmed and made more precise; R=0.2+/-0.1. Low-energy results in the MS-bar scheme, by contrast, show the typical pathologies of a non-convergent asymptotic series.

Improving perturbation theory via a variational optimization has generally produced in higher orders an embarrassingly large set of solutions, most of them unphysical (complex). We introduce an extension of the optimized perturbation method which leads to a drastic reduction of the number of acceptable solutions. The properties of this new method are studied and it is then applied to the calculation of relevant quantities in different $\phi^4$ models, such as the anharmonic oscillator energy levels and the critical Bose-Einstein Condensation temperature shift $\Delta T_c$ recently investigated by various authors. Our present estimates of $\Delta T_c$, incorporating the most recently available six and seven loop perturbative information, are in excellent agreement with all the available lattice numerical simulations. This represents a very substantial improvement over previous treatments.

We investigate a system of frustrated hardcore bosons, modeled by an XY antiferromagnet on the spatially anisotropic triangular lattice, using Takahashi's modified spin-wave (MSW) theory. In particular we implement ordering vector optimization on the ordered reference state of MSW theory, which leads to significant improvement of the theory and accounts for quantum corrections to the classically ordered state. The MSW results at zero temperature compare favorably to exact diagonalization (ED) and projected entangled-pair state (PEPS) calculations. The resulting zero-temperature phase diagram includes a 1D quasi-ordered phase, a 2D Neel ordered phase, and a 2D spiraling ordered phase. We have strong indications that the various ordered or quasi-ordered phases are separated by spin-liquid phases with short-range correlations, in analogy to what has been predicted for the Heisenberg model on the same lattice. Within MSW theory we also explore the finite-temperature phase diagram. We find that the zero-temperature long-range-ordered phases turn into quasi-ordered phases (up to a Berezinskii-Kosterlitz-Thouless temperature), while zero-temperature quasi-ordered phases become short-range correlated at finite temperature. These results show that modified spin-wave theory is very well suited for describing ordered and quasi-ordered phases of frustrated XY spins (or, equivalently, of frustrated lattice bosons) both at zero and finite temperatures. While MSW theory, just as other theoretical methods, cannot describe spin-liquid phases, its breakdown provides a fast method for singling out Hamiltonians which may feature these intriguing quantum phases. We thus suggest a tool for guiding our search for interesting systems whose properties are necessarily studied with a physical quantum simulator.

We study the ground state phases of the $S=1/2$ Heisenberg quantum antiferromagnet on the spatially anisotropic triangular lattice and on the square lattice with up to next-next-nearest neighbor coupling (the $J_1J_2J_3$ model), making use of Takahashi's modified spin-wave (MSW) theory supplemented by ordering vector optimization. We compare the MSW results with exact diagonalization and projected-entangled-pair-states calculations, demonstrating their qualitative and quantitative reliability. We find that MSW theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular collinear magnetic order is promoted at the expenses of non-collinear (spiral) order, and several spiral states which are stable at the classical level, disappear from the quantum phase diagram. Moreover, collinear states and non-collinear ones are never connected continuously, but they are separated by parameter regions in which MSW breaks down, signaling the possible appearance of a non-magnetic ground state. In the case of the spatially anisotropic triangular lattice, a large breakdown region appears also for weak couplings between the chains composing the lattice, suggesting the possible occurrence of a large non-magnetic region continuously connected with the spin-liquid state of the uncoupled chains.

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean-variance optimal portfolios. It is shown that the solutions of the Markowitz optimization problem and the quadratic utility problem are not always mean-variance efficient. The conditions for the mean-variance efficiency of the solutions depend on the unknown parameters of the asset returns. We deal with the problem of parameter uncertainty in detail and derive the probabilities that the estimated solutions of the Markowitz problem and the quadratic utility problem are mean-variance efficient. Because these probabilities deviate from one the above mentioned quadratic optimization problems are not stochastically equivalent. The obtained results are illustrated by an empirical study.

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean-variance optimal portfolios. It is shown that the solutions of the Markowitz optimization problem and the quadratic utility problem are not always mean-variance efficient. The conditions for the mean-variance efficiency of the solutions depend on the unknown parameters of the asset returns. We deal with the problem of parameter uncertainty in detail and derive the probabilities that the estimated solutions of the Markowitz problem and the quadratic utility problem are mean-variance efficient. Because these probabilities deviate from one the above mentioned quadratic optimization problems are not stochastically equivalent. The obtained results are illustrated by an empirical study.

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean-variance optimal portfolios. It is shown that the solutions of the Markowitz optimization problem and the quadratic utility problem are not always mean-variance efficient. The conditions for the mean-variance efficiency of the solutions depend on the unknown parameters of the asset returns. We deal with the problem of parameter uncertainty in detail and derive the probabilities that the estimated solutions of the Markowitz problem and the quadratic utility problem are mean-variance efficient. Because these probabilities deviate from one the above mentioned quadratic optimization problems are not stochastically equivalent. The obtained results are illustrated by an empirical study.

A working theory of two-component two-phase (gas-liquid) nozzles, developed as part of Phase I, was used to conduct parametric performance analyses over a wide range of flow conditions and for varied fluid properties. Droplet breakup and the interface transport of momentum and thermal energy were considered in the analyses, but mass transfer and wall friction losses were excluded. Results from the parametric analyses compare favorably with experimental data and other theoretical analyses available in the literature. The sensitivity of the predicted nozzle performance to the assumptions concerning the droplet characteristics was examined, and criteria were developed for optimum nozzle designs based on the parametric analyses. A simplified procedure was developed for the quick estimation of the major dimensions for two-phase nozzles. Finally, the work extraction potential of two-phase nozzles was examined in terms of their performance criteria and system integration characteristics.

The research described in this report deals with the development of (1) efficient, consistent discretization techniques for use in semi-infinite optimization, optimal control algorithms that solve problems with dynamics governed by partial differential equations, (2) superlinearly converging semi- finite optimization algorithms, (3) various techniques for finding design parameters satisfying specifications, (4) optimal control algorithms for discrete and distributed systems with control, state and shape constraints, and (5) efficient numerical procedures for the integrated design of flexible structures and their control systems.... Optimization, Optimal shape design algorithms.

General perturbations theory applications to spacecraft guidance, flight mechanics, and trajectory optimization

A working theory of two-component two-phase (gas-liquid) nozzles, developed as part of Phase I, was used to conduct parametric performance analyses over a wide range of flow conditions and for varied fluid properties. Droplet breakup and the interface transport of momentum and thermal energy were considered in the analyses, but mass transfer and wall friction losses were excluded. Results from the parametric analyses compare favorably with experimental data and other theoretical analyses available in the literature. The sensitivity of the predicted nozzle performance to the assumptions concerning the droplet characteristics was examined, and criteria were developed for optimum nozzle designs based on the parametric analyses. A simplified procedure was developed for the quick estimation of the major dimensions for two-phase nozzles. Finally, the work extraction potential of two-phase nozzles was examined in terms of their performance criteria and system integration characteristics.

The paper treats an extension of one version of the classical Lagrange multiplier rule as applied to nonlinear programming problems. For a given problem, an auxiliary problem is defined and its properties are studied under various assumptions. In particular, when the given problem has a strictly convex objective function and concave constraints it is shown that the auxiliary problem is one of maximizing a concave differentiable function over an open set subject only to nonnegativity conditions. Some applications of this theory are presented only with the connection between the auxiliary problem and a 'dual' of the given problem.

Contents: Differential Calculus in Normed Linear Spaces; Minimisation of Functionals; Minimisation Without Constraints; Minimization with Constraints; Duality and Its Applications; Elements of the Theory of Control. Lecture Notes Collection FreeScience.info ID2729 Obtained from http://www.math.tifr.res.in/~publ/ln/tifr53.pdf http://www.freescience.info/go.php?pagename=books&id=2729

Contents: Differential Calculus in Normed Linear Spaces; Minimisation of Functionals; Minimisation Without Constraints; Minimization with Constraints; Duality and Its Applications; Elements of the Theory of Control. Lecture Notes Collection FreeScience.info ID2729 Obtained from http://www.math.tifr.res.in/~publ/ln/tifr53.pdf http://www.freescience.info/go.php?pagename=books&id=2729

Research on College English Teaching Optimization Driven by Embodied Theory to Generate Ideological and Political Effectiveness

Mathematical Optimization and Economic Theory provides a self-contained introduction to and survey of mathematical programming and control techniques and their applications to static and dynamic problems in economics, respectively. It is distinctive in showing the unity of the various approaches to solving problems of constrained optimization that all stem back directly or indirectly to the method of Lagrange multipliers. In the 30 years since its initial publication, there have been many more applications of these mathematical techniques in economics, as well as some advances in the mathematics of programming and control. Nevertheless, the basic techniques remain the same today as when the book was originally published. Thus, it continues to be useful not only to its original audience of advanced undergraduate and graduate students in economics, but also to mathematicians and other researchers who are interested in learning about the applications of the mathematics of optimization to economics. The book is distinctive in that it covers in some depth both static programming problems and dynamic control problems of optimization and the techniques of their solution. It also clearly presents many applications of these techniques to economics, and it shows why optimization is important for economics. Many challenging problems for both students and researchers are included.

Journal of Optimization Theory and Applications 1996: Volume 91 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1996-09_90_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1996-10_91_1 .

Journal of Optimization Theory and Applications 1996: Volume 91 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1996-09_90_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1996-10_91_1 .

Journal of Optimization Theory and Applications 1996: Volume 91 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1996-09_90_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1996-10_91_1 .

Journal of Optimization Theory and Applications 1991: Volume 70 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1991-06_69_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1991-07_70_1 .

Journal of Optimization Theory and Applications 1995: Volume 87 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1995-09_86_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1995-10_87_1 .

Journal of Optimization Theory and Applications 1996: Volume 89 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1996-03_88_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1996-04_89_1 .