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We illustrate the utility of the recently developed loop calculus for improving the Belief Propagation (BP) algorithm. If the algorithm that minimizes the Bethe free energy fails we modify the free energy by accounting for a critical loop in a graphical representation of the code. The log-likelihood specific critical loop is found by means of the loop calculus. The general method is tested using an example of the Linear Programming (LP) decoding, that can be viewed as a special limit of the BP decoding. Considering the (155,64,20) code that performs over Additive-White-Gaussian-Noise channel we show that the loop calculus improves the LP decoding and corrects all previously found dangerous configurations of log-likelihoods related to pseudo-codewords with low effective distance, thus reducing the code's error-floor.

In this paper we present a new Turbo analog error correcting coding scheme for real valued signals that are corrupted by impulsive noise. This Turbo code improves Donoho's deterministic construction by using a probabilistic approach. More specifically, our construction corrects more errors than the matrices of Donoho by allowing a vanishingly small probability of error (with the increase in block size). The problem of decoding the long block code is decoupled into two sets of parallel Linear Programming problems. This leads to a significant reduction in decoding complexity as compared to one-step Linear Programming decoding.

In this paper we present a new Turbo analog error correcting coding scheme for real valued signals that are corrupted by impulsive noise. This Turbo code improves Donoho's deterministic construction by using a probabilistic approach. More specifically, our construction corrects more errors than the matrices of Donoho by allowing a vanishingly small probability of error (with the increase in block size). The problem of decoding the long block code is decoupled into two sets of parallel Linear Programming problems. This leads to a significant reduction in decoding complexity as compared to one-step Linear Programming decoding.

In this paper we present a new Turbo analog error correcting coding scheme for real valued signals that are corrupted by impulsive noise. This Turbo code improves Donoho's deterministic construction by using a probabilistic approach. More specifically, our construction corrects more errors than the matrices of Donoho by allowing a vanishingly small probability of error (with the increase in block size). The problem of decoding the long block code is decoupled into two sets of parallel Linear Programming problems. This leads to a significant reduction in decoding complexity as compared to one-step Linear Programming decoding.

In this paper, we present an improved union bound on the Linear Programming (LP) decoding performance of the binary linear codes transmitted over an additive white Gaussian noise channels. The bounding technique is based on the second-order of Bonferroni-type inequality in probability theory, and it is minimized by Prim's minimum spanning tree algorithm. The bound calculation needs the fundamental cone generators of a given parity-check matrix rather than only their weight spectrum, but involves relatively low computational complexity. It is targeted to high-density parity-check codes, where the number of their generators is extremely large and these generators are spread densely in the Euclidean space. We explore the generator density and make a comparison between different parity-check matrix representations. That density effects on the improvement of the proposed bound over the conventional LP union bound. The paper also presents a complete pseudo-weight distribution of the fundamental cone generators for the BCH[31,21,5] code.

The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of (mixed strategy) Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of (mixed strategy) Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of (mixed strategy) Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of (mixed strategy) Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of (mixed strategy) Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

Bibliography: leaf 9

An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.

We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some recent concentration of measure results. The linear programming inequality may be of independent interest.

We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some recent concentration of measure results. The linear programming inequality may be of independent interest.

ADA721562

45 p. 28 cm

Available from National Technical Information Service, Springfield, Va

This paper studies the linear optimization problem subject to a system of bipolar fuzzy relation equations with the max-product composition operator. Its feasible domain is briefly characterized by its lower and upper bound, and its consistency is considered. Also, some sufficient conditions are proposed to reduce the size of the search domain of the optimal solution to the problem. Under these conditions, some equations can be deleted to compute the minimum objective value. Some sufficient conditions are then proposed which under them, one of the optimal solutions of the problem is explicitly determined and the uniqueness conditions of the optimal solution are expressed. Moreover, a modified branch-and-bound method based on a value matrix is proposed to solve the reduced problem. A new algorithm is finally designed to solve the problem based on the conditions and modified branch-and-bound method. The algorithm is compared to the methods in other papers to show its efficiency.

The United States Army is facing a significant challenge to maintain the training readiness of its force. The supply of training land has not significantly increased since the end of World War II; whereas the demand for training land has substantially inc

To assess the degree of practical implementation of the optimization principle when comparing options for plans compiled in different ways, this paper proposes a comprehensive indicator of the effectiveness of planned calculations. The advantage of the indicator is that its value is proportional to the magnitude of potential losses from incomplete and incomplete use of available resources, that is, those factors that symbolize the loss of resources in the economic planning process, but have not yet served as criteria for the quality of planning decisions. Therefore, the fact that the optimization method makes it possible to improve (reduce) the value of these indicators with the same volumes of available production resources allows us to conclude that the structural optimization method is very effective and promising in solving production problems of linear programming and in the process of economic planning.

To assess the degree of practical implementation of the optimization principle when comparing options for plans compiled in different ways, this paper proposes a comprehensive indicator of the effectiveness of planned calculations. The advantage of the indicator is that its value is proportional to the magnitude of potential losses from incomplete and incomplete use of available resources, that is, those factors that symbolize the loss of resources in the economic planning process, but have not yet served as criteria for the quality of planning decisions. Therefore, the fact that the optimization method makes it possible to improve (reduce) the value of these indicators with the same volumes of available production resources allows us to conclude that the structural optimization method is very effective and promising in solving production problems of linear programming and in the process of economic planning.

Available from National Technical Information Service, Springfield, Va

Since 1988, the United States Army has closed 112 and has completed or will soon complete realignment of another 27 of its domestic installations. The Army estimates the total cost (between 1988 and 2001) of these closures and realignments to be $5.3 billion, of which about $2.3 billion (43%) is associated with environmental cleanup. Beyond 2001, the Army expects to spend an additional $ 1.09 billion to complete cleanup and continue restoration. The Army Base Realignment and Closure Office (BRACO) is currently funding environmental cleanup at 649 sites on 39 current and former Army installations. BRACO' 5 environmental restoration budget from 2001 to 2007 to support cleanup at these installations (totaling over $620 million) is not sufficient to support each installation's requirement for those years. Considering environmental policies and yearly funding requests from 2001 to 2015 for each site, this thesis develops optimization models and a spreadsheet interface to help BRACO allocate its budget. Model results prescribe either funding each site as requested or delaying cleanup by one to five years. Extensive model use helped BRACO analyze alternate yearly budgets, suggest alternate site funding and determine site funding for 2001 to 2007

Bibliography: p. 91

R\'esum\'e Apr\`es un bref aper\c{c}u permettant de situer notre travail, nous proposons une nouvelle voie pour aborder la programmation lin\'eaire en proposant un algorithme \'elabor\'e \`a partir d'une id\'ee simple qui permet d'obtenir une solution aussi approch\'ee que voulu par translation dichotomique d'un hyperplan de l'espace des solutions. Abstract After a short course in order to situate our work, we propose a new way to study linear programming and we give a proposal of algorithm to solve linear programming from a basic idea which allow to obtain an approached solution with desired accuracy. For this we use some dichotomic translations of an hyperplan in the solutions hyperspace.

We present and study linear programming based detectors for two-dimensional intersymbol interference channels. Interesting instances of two-dimensional intersymbol interference channels are magnetic storage, optical storage and Wyner's cellular network model. We show that the optimal maximum a posteriori detection in such channels lends itself to a natural linear programming based sub-optimal detector. We call this the Pairwise linear program detector. Our experiments show that the Pairwise linear program detector performs poorly. We then propose two methods to strengthen our detector. These detectors are based on systematically enhancing the Pairwise linear program. The first one, the Block linear program detector adds higher order potential functions in an {\em exhaustive} manner, as constraints, to the Pairwise linear program detector. We show by experiments that the Block linear program detector has performance close to the optimal detector. We then develop another detector by {\em adaptively} adding frustrated cycles to the Pairwise linear program detector. Empirically, this detector also has performance close to the optimal one and turns out to be less complex then the Block linear program detector.

The United States Armed Forces must be capable of deploying to areas of operations anywhere is the world. Planning for these deployments is the responsibility of the Joint Deployment Agency, MacDill Air Force Base, Tampa, Florida. Deployment plans are large and complex. A straightforward linear programming model of a deployment plan could easily exceed 700 million decision variables. This study outlines the development of a system used to assist planners in determining deployment plan feasibility and in selecting modes of transportation. The system consists of a data input array, an algorithm to eliminate all unusable variables, and a linear programming model. The largest scenario in this study is a 90-day deployment plan with 80 movement requirements, 9 types of lift assets, traveling between 22 ports. This corresponds to a linear programming model with 35 million decision variables. The variable reduction algorithm reduced the number of variables to 11,100, and an optimal solution was found in a total computation time (input, reduction, optimization, output) time of 6.5 minutes.

Linear and Nonlinear Programming by David G.Luenberger and Yinyu Ye

This volume was digitized and made accessible online due to deterioration of the original print copy.

Bibliography: leaves 38-39

The facial reduction algorithm of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program $$ (P) \sup { | Ax \leq_K b} $$ in the absence of any constraint qualification. The facial reduction algorithm solves a sequence of auxiliary optimization problems to obtain such a dual. Ramana's dual is applicable when (P) is a semidefinite program (SDP) and is an explicit SDP itself. Ramana, Tuncel, and Wolkowicz showed that these approaches are closely related; in particular, they proved the correctness of Ramana's dual using certificates from a facial reduction algorithm. Here we give a clear and self-contained exposition of facial reduction, of extended duals, and generalize Ramana's dual: -- we state a simple facial reduction algorithm and prove its correctness; and -- building on this algorithm we construct a family of extended duals when $K$ is a {\em nice} cone. This class of cones includes the semidefinite cone and other important cones.

Polar codes are high density parity check codes and hence the sparse factor graph, instead of the parity check matrix, has been used to practically represent an LP polytope for LP decoding. Although LP decoding on this polytope has the ML-certificate property, it performs poorly over a BAWGN channel. In this paper, we propose modifications to adaptive cut generation based LP decoding techniques and apply the modified-adaptive LP decoder to short blocklength polar codes over a BAWGN channel. The proposed decoder provides significant FER performance gain compared to the previously proposed LP decoder and its performance approaches that of ML decoding at high SNRs. We also present an algorithm to obtain a smaller factor graph from the original sparse factor graph of a polar code. This reduced factor graph preserves the small check node degrees needed to represent the LP polytope in practice. We show that the fundamental polytope of the reduced factor graph can be obtained from the projection of the polytope represented by the original sparse factor graph and the frozen bit information. Thus, the LP decoding time complexity is decreased without changing the FER performance by using the reduced factor graph representation.

A linear programing model and procedures for optimal assignment of students to attendance centers are presented. An example of the use of linear programing for the assignment of students to attendance centers in a particular school district is given. (CK)

A linear programing model and procedures for optimal assignment of students to attendance centers are presented. An example of the use of linear programing for the assignment of students to attendance centers in a particular school district is given. (CK)

A linear programing model and procedures for optimal assignment of students to attendance centers are presented. An example of the use of linear programing for the assignment of students to attendance centers in a particular school district is given. (CK)

From the bitsavers.org collection, a scanned-in computer-related document. ibm :: 1620 :: programs :: 10.1.008 Linear Programming II

We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of these.

By leveraging advanced techniques and models, Operations Research (OR) provides critical insights and strategic interventions across multiple domains, including transportation, communication, project management, and supply chain optimization. The field's multifaceted approach continues to drive efficiency and innovation in numerous industries. This paper thoroughly evaluates numerous approaches and methods researchers employ to model and investigate problems. Our objective is to bridge gaps in existing literature by examining recent advancements in this field. Network flow problems encompass the shortest path, maximal cost flow, and minimal cost flow problems. These critical elements are essential for understanding transportation dynamics, communication, and resource allocation networks. Furthermore, we explore real-life scenarios where these network flow problems arise, shedding light on their practical significance.

This volume was digitized and made accessible online due to deterioration of the original print copy.

Thesis (M.S. in Comp. Sci. & M.S. in Operations Research)--Naval Postgraduate School, 1977

The objective of this project was to write computer code to perform linear programming and quadratic programming minimization tasks, for eventual inclusion in a robotic control system. The basic concept underlying the project is this: given a description of a robot and a description of an object in the robot's surrounding in terms of a series of inequalities, the minimization code can find the minimum distance between the robot and the object. The linear programming algorithm minimizes the infinity norm, while the quadratic programming algorithm mimimizes the euclidian norm. The programming language 'C' was used to implement both programming algorithms, due to its natural speed, combined with the ability to use different floating point libraries at will. An added advantage of using 'C' on the sun workstations is the ability to make use of the 68881 floating point coprocessor on the Sun 3 computers, which provides dramatic speed increases over using floating point libraries. Each programming algorithm was implemented as a function, along with its supporting subroutines. For ease of development, each algorithm was developed in a separate program. However, there should be no difficulty in incorporating either the linear programming algorithm or the quadratic programming algorithm into a larger section of code when implementing a robotic control system.

Method and Validation for Optimal Lineup Creation for Daily Fantasy Football Using Machine Learning and Linear Programming

Bibliography: leaf 51

Bibliography: leaf 51

This paper describes an approach to faculty timetabling and course scheduling that uses computerized linear programming. After reviewing the literature on linear programming, the paper discusses the process whereby a timetable was created for a department at the University of New Brunswick. Faculty were surveyed with respect to course offerings and preferred days and times of instruction. Variables were then constructed and data entered using the IBM Mathematical Programming System (MPS) on a mainframe computer. For a department of 13 faculty members the result was a set of 200 variables, about 35 of which were to be selected through linear programming to form the basis for determining feasible and optimal section offerings for the timetabling period. Several timetables and lists were prepared for faculty members to review, with their comments used to adjust the program to produce the most acceptable results for the department as a whole. Application of this process at the university and secondary school level is discussed. (Contains 30 references.) (MDM)