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Multiple criteria approaches to decision situations are receiving increased popularity due to the increasing importance society places on incorporating the non-commensurate and conflicting objectives of a situation into the choice making process. Process algorithms for multiple objective optimization theory (MOOT) and multiple attribute utility theory (MAUT) are presented at a theoretical level as well as at the application level in a systems engineering framework appropriate for choice making. A subsequent comparison of two approaches motivated a combined MOOT/MAUT methodology which utilizes, in an efficient manner, the complementary aspects of both processes. Results are presented of the application of this joint approach to a defense system acquisition problem. Specifically, a paradigm for electronic warfare aircraft retrofit was developed using the combined multicritera MOOT/MAUT process. A set of criteria was developed in this application which can be used to evaluate, in a comprehensive manner, alternative system configurations. (Author)

In systems with hard real-time constraints, it is necessary to compute upper bounds on the worst-case execution time (WCET) of programs; the closer the bound to the real WCET, the better. This is especially the case of synchronous reactive control loops with a fixed clock; the WCET of the loop body must not exceed the clock period. We compute the WCET (or at least a close upper bound thereof) as the solution of an optimization modulo theory problem that takes into account the semantics of the program, in contrast to other methods that compute the longest path whether or not it is feasible according to these semantics. Optimization modulo theory extends satisfiability modulo theory (SMT) to maximization problems. Immediate encodings of WCET problems into SMT yield formulas intractable for all current production-grade solvers; this is inherent to the DPLL(T) approach to SMT implemented in these solvers. By conjoining some appropriate "cuts" to these formulas, we considerably reduce the computation time of the SMT-solver. We experimented our approach on a variety of control programs, using the OTAWA analyzer both as baseline and as underlying microarchitectural analysis for our analysis, and show notable improvement on the WCET bound on a variety of benchmarks and control programs.

In systems with hard real-time constraints, it is necessary to compute upper bounds on the worst-case execution time (WCET) of programs; the closer the bound to the real WCET, the better. This is especially the case of synchronous reactive control loops with a fixed clock; the WCET of the loop body must not exceed the clock period. We compute the WCET (or at least a close upper bound thereof) as the solution of an optimization modulo theory problem that takes into account the semantics of the program, in contrast to other methods that compute the longest path whether or not it is feasible according to these semantics. Optimization modulo theory extends satisfiability modulo theory (SMT) to maximization problems. Immediate encodings of WCET problems into SMT yield formulas intractable for all current production-grade solvers; this is inherent to the DPLL(T) approach to SMT implemented in these solvers. By conjoining some appropriate "cuts" to these formulas, we considerably reduce the computation time of the SMT-solver. We experimented our approach on a variety of control programs, using the OTAWA analyzer both as baseline and as underlying microarchitectural analysis for our analysis, and show notable improvement on the WCET bound on a variety of benchmarks and control programs.

Purpose:  This study aimed to optimize the stock portfolio based on stochastic matrix theory in the stock market and to answer whether the relevant information will exist using the Marčenko–Pastur distribution. Methodology:  The data of 31 shares in the Tehran Stock Exchange in 2016 - 2019 will be examined for cross-correlation between shares. So, there will be 749 end-of-day prices and 748 logarithms of returns. This research was done using the descriptive-correlation method and is of an applied research type. Findings:  The results showed: a) Observing the most extensive distribution of eigenvector components, it can be seen that there is a solid asymmetry to the left of the distribution, meaning that the market responds more to bad events than good events. b) By clearing the correlation matrix, the difference between the predicted and realized risk can be slightly reduced. In other words, the risk is reduced by identifying and removing non-valuable stocks from the portfolio portfolio. c) A stochastic stock matrix can significantly predict the realized return and risk of the market and, therefore, explain the risk of market information. d) The inverse participation ratio determines the stocks affecting the particular vectors, and the primary analysis of random matrices is based on adjusting this ratio using random matrix clearance. Originality/Value:  Unlike other portfolio formation methods determining the weight of each asset in the portfolio,   stochastic matrix theory identifies unused stocks and removes them from the stock portfolio, thereby improving portfolio return and risk.

Purpose:  This study aimed to optimize the stock portfolio based on stochastic matrix theory in the stock market and to answer whether the relevant information will exist using the Marčenko–Pastur distribution. Methodology:  The data of 31 shares in the Tehran Stock Exchange in 2016 - 2019 will be examined for cross-correlation between shares. So, there will be 749 end-of-day prices and 748 logarithms of returns. This research was done using the descriptive-correlation method and is of an applied research type. Findings:  The results showed: a) Observing the most extensive distribution of eigenvector components, it can be seen that there is a solid asymmetry to the left of the distribution, meaning that the market responds more to bad events than good events. b) By clearing the correlation matrix, the difference between the predicted and realized risk can be slightly reduced. In other words, the risk is reduced by identifying and removing non-valuable stocks from the portfolio portfolio. c) A stochastic stock matrix can significantly predict the realized return and risk of the market and, therefore, explain the risk of market information. d) The inverse participation ratio determines the stocks affecting the particular vectors, and the primary analysis of random matrices is based on adjusting this ratio using random matrix clearance. Originality/Value:  Unlike other portfolio formation methods determining the weight of each asset in the portfolio,   stochastic matrix theory identifies unused stocks and removes them from the stock portfolio, thereby improving portfolio return and risk.

Journal of Optimization Theory and Applications 1979: Volume 28 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1979_28_index . Next issue: sim_journal-of-optimization-theory-and-applications_1979-05_28_1 .

Journal of Optimization Theory and Applications 1981: Volume 34 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1981-04_33_4 . Next issue: sim_journal-of-optimization-theory-and-applications_1981-05_34_1 .

Journal of Optimization Theory and Applications 1982: Volume 38 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1982-08_37_4 . Next issue: sim_journal-of-optimization-theory-and-applications_1982-09_38_1 .

Journal of Optimization Theory and Applications 1986: Volume 51 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1986-09_50_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1986-10_51_1 .

Journal of Optimization Theory and Applications 1988: Volume 57 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1988-03_56_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1988-04_57_1 .

Journal of Optimization Theory and Applications 1993: Volume 76 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1992-12_75_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1993-01_76_1 .

Journal of Optimization Theory and Applications 1993: Volume 76 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1992-12_75_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1993-01_76_1 .

Journal of Optimization Theory and Applications 1993: Volume 76 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1992-12_75_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1993-01_76_1 .

This paper presents a canonical d.c. (difference of canonical and convex functions) programming problem, which can be used to model general global optimization problems in complex systems. It shows that by using the canonical duality theory, a large class of nonconvex minimization problems can be equivalently converted to a unified concave maximization problem over a convex domain, which can be solved easily under certain conditions. Additionally, a detailed proof for triality theory is provided, which can be used to identify local extremal solutions. Applications are illustrated and open problems are presented.

The method of steepest descent used in optimizing one-dimensional layered radiation shields is extended to multidimensional, multiconstraint situations. The multidimensional optimization algorithm and equations are developed for the case of a dose constraint in any one direction being dependent only on the shield thicknesses in that direction and independent of shield thicknesses in other directions. Expressions are derived for one-, two-, and three-dimensional cases (one, two, and three constraints). The precedure is applicable to the optimization of shields where there are different dose constraints and layering arrangements in the principal directions.

The main purpose of this research note is to show that the triality theory can always be used to identify both global minimizer and the biggest local maximizer in global optimization. An open problem left on the double-min duality is solved for a nonconvex optimization problem with double-well potential in $\real^n$, which leads to a complete set of analytical solutions. Also a convergency theorem is proved for linear perturbation canonical dual method, which can be used for solving global optimization problems with multiple solutions. The methods and results presented in this note pave the way towards the proof of the triality theory in general cases.

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 1978: Volume 24 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1978_24_index . Next issue: sim_journal-of-optimization-theory-and-applications_1978-01_24_1 .

Journal of Optimization Theory and Applications 1983: Volume 40 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1983-04_39_4 . Next issue: sim_journal-of-optimization-theory-and-applications_1983-05_40_1 .

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Journal of Optimization Theory and Applications 1988: Volume 56 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1987-12_55_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1988-01_56_1 .

Journal of Optimization Theory and Applications 1995: Volume 86 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1995-06_85_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1995-07_86_1 .

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Journal of Optimization Theory and Applications 1975: Volume 15 , Issue Index. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1974-12_14_6 . Next issue: sim_journal-of-optimization-theory-and-applications_1975-01_15_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 .

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Journal of Optimization Theory and Applications 1980: Volume 31 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1980-04_30_4 . Next issue: sim_journal-of-optimization-theory-and-applications_1980-05_31_1 .

Journal of Optimization Theory and Applications 1996: Volume 88 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1995-12_87_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1996-01_88_1 .

Journal of Optimization Theory and Applications 2002: Volume 115 , Issue Contents. Digitized from IA1534532-02 . Previous issue: sim_journal-of-optimization-theory-and-applications_2002-09_114_3 . Next issue: sim_journal-of-optimization-theory-and-applications_2002-10_115_1 .

xv, 391 p. 24 cm

Stepper motors are broadly utilized in actual systems, which are marked by non-linear parameters such as internal, external noises and uncertainties from wireless network. As well, a suitable controller is required when the problem is to track the target signal. In this paper, robust controller based on model reference are investigated to wireless control and optimize position and time in stepper motors. The core impression to build a robust controller is to use a model reference control system. Furthermore, simulations are implemented to control stepper motor position and time in two cases: first, when the wireless network without any delay and packet dropout. Second, uncertain equations when the wireless network with time delays and packet dropout. Simulation results demonstrate that proposed controller has achieved and enhanced the performance in tracking and robustness.

Stepper motors are broadly utilized in actual systems, which are marked by non-linear parameters such as internal, external noises and uncertainties from wireless network. As well, a suitable controller is required when the problem is to track the target signal. In this paper, robust controller based on model reference are investigated to wireless control and optimize position and time in stepper motors. The core impression to build a robust controller is to use a model reference control system. Furthermore, simulations are implemented to control stepper motor position and time in two cases: first, when the wireless network without any delay and packet dropout. Second, uncertain equations when the wireless network with time delays and packet dropout. Simulation results demonstrate that proposed controller has achieved and enhanced the performance in tracking and robustness.

Stepper motors are broadly utilized in actual systems, which are marked by non-linear parameters such as internal, external noises and uncertainties from wireless network. As well, a suitable controller is required when the problem is to track the target signal. In this paper, robust controller based on model reference are investigated to wireless control and optimize position and time in stepper motors. The core impression to build a robust controller is to use a model reference control system. Furthermore, simulations are implemented to control stepper motor position and time in two cases: first, when the wireless network without any delay and packet dropout. Second, uncertain equations when the wireless network with time delays and packet dropout. Simulation results demonstrate that proposed controller has achieved and enhanced the performance in tracking and robustness.

The main objective of this has been the development awl maturation of a adjoint-based, viscous design techniques for Aerodynamic Shape Optimization (ASO) of complete aircraft configurations. We have followed a systematic approach in the development, validation and testing of our methods. In addition, we have carried out some preliminary work in the development of a mathematical environment for high-fidelity aero-structural optimization as a first step towards the realization of a high-fidelity multidisciplinary optimization disability. A number of significant milestones achieved in this process are detailed in the final report.

A global convergence theory for a class of trust-region algorithms for solving the equality constrained optimization problem is presented. This theory is suffidently general that it holds for any algorithm that generates steps that give at least a fraction of Cauchy decrease in the quadratic model of the con- straints and uses the augmented Lagrangian as a merit function. This theory is used to establish global convergence of the 1g84 Celis-Dennis-Tapia algorithm with a different scheme for updating the penalty parameter. The behavior of the penalty parameter is also discussed.

This document serves as a final technical report for the AFOSR award F49620-95-1-0259. It reviews the formulation and application of optimization techniques based on control theory for aerodynamic shape design in viscous compressible flow. The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. Each design cycle requires the numerical solution of both the flow and the adjoint equations, leading to a computational cost roughly equal to the cost of two flow solutions. Representative results are presented for viscous optimization of transonic wing-body combinations.

This document serves as a final technical report for the AFOSR award F49620-95-1-0259. It reviews the formulation and application of optimization techniques based on control theory for aerodynamic shape design in viscous compressible flow. The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. Each design cycle requires the numerical solution of both the flow and the adjoint equations, leading to a computational cost roughly equal to the cost of two flow solutions. Representative results are presented for viscous optimization of transonic wing-body combinations.

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.

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.

Stochastic Resonance (SR) is a phenomenon that performance of the nonlinear system can be improved with the addition of optimal amount of noise. Stochastic resonance has been increasingly used for signal processing. The output of the nonlinear bistable dynamic system can be used to restore the weak input signal corrupted by white Gaussian noise, if the similarity between the input signal and the output can be maximized. This paper will first use the optimization theory to show that the normalized power norm (CI) describing the similarity will reach a larger maximum when tuning both the system parameters and noise intensity, compared with that of only adjusting noise intensity (classical stochastic resonance) of only adjusting system parameters (parameter-tuning stochastic resonance). Then, a practical fast-converging optimization algorithm is mentioned to search the optimal system parameters and noise intensity. Finally, computer simulations are performed to verify this proposal and demonstrate its application in signal processing.

Supported by this grant, the PI and his group have successfully solved a series of challenging problems in computer science, global optimization and applied mathematics, including the well-known NP-hard max-cut problem and sensor location problem in network optimization. An open problem on triality theory left in 2003 has been solved. This theory can be used to identify both global and local extremal solutions and to design powerful algorithms for solving real-world problems. Within the past five years, 2 books, 5 journal special issues, and about 60 papers have been published. Four international conferences have been organized, including the 3rd World Congress of Global Optimization. A unified methodology and algorithm have been developed with real-world applications. This grant has been used to support and co-support three post-doctors, three PhD students, one part-time senior researcher, and more than 15 short-time visitors. The PI has been invited to delivery 18 plenary/keynote lectures at international conferences. The projects proposed in the proposal have been fully completed. The canonical duality theory is now considering as a breakthrough new methodological theory in multidisciplinary fields of applied mathematics, global optimization and nonlinear mechanics.

Supported by this grant, the PI and his group have successfully solved a series of challenging problems in computer science, global optimization and applied mathematics, including the well-known NP-hard max-cut problem and sensor location problem in network optimization. An open problem on triality theory left in 2003 has been solved. This theory can be used to identify both global and local extremal solutions and to design powerful algorithms for solving real-world problems. Within the past five years, 2 books, 5 journal special issues, and about 60 papers have been published. Four international conferences have been organized, including the 3rd World Congress of Global Optimization. A unified methodology and algorithm have been developed with real-world applications. This grant has been used to support and co-support three post-doctors, three PhD students, one part-time senior researcher, and more than 15 short-time visitors. The PI has been invited to delivery 18 plenary/keynote lectures at international conferences. The projects proposed in the proposal have been fully completed. The canonical duality theory is now considering as a breakthrough new methodological theory in multidisciplinary fields of applied mathematics, global optimization and nonlinear mechanics.

Supported by this grant, the PI and his group have successfully solved a series of challenging problems in computer science, global optimization and applied mathematics, including the well-known NP-hard max-cut problem and sensor location problem in network optimization. An open problem on triality theory left in 2003 has been solved. This theory can be used to identify both global and local extremal solutions and to design powerful algorithms for solving real-world problems. Within the past five years, 2 books, 5 journal special issues, and about 60 papers have been published. Four international conferences have been organized, including the 3rd World Congress of Global Optimization. A unified methodology and algorithm have been developed with real-world applications. This grant has been used to support and co-support three post-doctors, three PhD students, one part-time senior researcher, and more than 15 short-time visitors. The PI has been invited to delivery 18 plenary/keynote lectures at international conferences. The projects proposed in the proposal have been fully completed. The canonical duality theory is now considering as a breakthrough new methodological theory in multidisciplinary fields of applied mathematics, global optimization and nonlinear mechanics.

Canonical duality-triality is a breakthrough methodological theory, which can be used not only for modeling complex systems within a unified framework, but also for solving a wide class of challenging problems from real-world applications. This paper presents a brief review on this theory, its philosophical origin, physics foundation, and mathematical statements in both finite and infinite dimensional spaces, with emphasizing on its role for bridging the gap between nonconvex analysis/mechanics and global optimization. Special attentions are paid on unified understanding the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization, as well as the theorems, methods, and algorithms for solving these challenging problems. Misunderstandings and confusions on some basic concepts, such as objectivity, nonlinearity, Lagrangian, and generalized convexities are discussed and classified. Breakthrough from recent challenges and conceptual mistakes by M. Voisei, C. Zalinescu and his co-worker are addressed. Some open problems and future works in global optimization and nonconvex mechanics are proposed.

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.

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.

Inherent resource constraints within Mobile Ad Hoc Networks (MANETs) necessitate resource optimization, specifically power and rate control, as a critical focus for enhancing network performance in terms of energy, throughput, and delay. Although traditional power and rate control mechanisms have successfully improved throughput or energy efficiency, they fail to address the complex trade-offs between delay, energy consumption, and network stability, particularly in highly dynamic or unpredictable networks. Motivated by this, this study introduces a new Dynamic Power-Rate Optimization Grey Wolf Algorithm (DPRO-GWA) mechanism derived from a game-theoretic framework that balances outage probability and residual energy demands to achieve energy efficiency and quality of service (QoS) in mobile ad hoc networks (MANETs). The proposed approach formulates power and rate allocation as a super-modular game, which ensures both the existence and uniqueness of a Nash Equilibrium (NE) as the optimal solution for distributed non-cooperative nodes. We subsequently introduce an Adaptive Grey Wolf Optimizer (AGWO), which enhances the Grey Wolf Optimizer (GWO) by increasing convergence speed through adaptive tuning of the exploration-exploitation trade-off. Extensive simulation results demonstrate that DPRO-GWA significantly outperforms existing algorithms, including the Dynamic Rate and Power Allocation Algorithm (DRPAA), Energy Conserving Power and Rate Control (ECPRC), and Rate-Effective Network Utility Maximization (RENUM) in terms of energy consumption, throughput, and delay. Additionally, the proposed method maximizes the energy-delay trade-off, leading to considerable improvements in the network lifetime and performance, particularly in time-variant and fading channel environments. Thus, this study creates a promising avenue for refining power and rate control protocols for next-generation MANETs.