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About 10,000 papers for “Optimization and Mathematical Programming”

Entropy Optimization and Mathematical Programming

Shu‐Cherng Fang, Jay Rajasekera, H.-S. Jacob Tsao · International series in management science/operations research/International series in operations research & management science · 1997

Cited by 247

Optimization of the mathematical programming and applications

Johnny Moisés Valverde Montoro, Milton Milcíades Cortez Gutiérrez, Hernán Oscar Cortez Gutiérrez · South Florida Journal of Development · 2021

The present investigation responds to the need to solve optimization problems with optimality conditions. The KKT conditions are considered for multiobjective optimization problems with interval-valued objective functions.

Cited by 0Open access

Some contributions to mathematical programming and combinatorial optimization

José Neto · SPIRE - Sciences Po Institutional REpository · 2019

Consider the optimization (i.e. maximization or minimization) of a real valued function f defined on a subset of the n-dimensional real vector space, subject to some set of constraints on the variables. The present document gathers and summarizes part of the work I could carry out on such optimization problems when the objective function is either linear or quadratic and when the constraints set on the variables are linear and/or integrality constraints.In the first part, methods are presented to deal with general families of mathematical programs: (mixed-integer) linear programs and unconstrained binary quadratic programs, namely. Chapter 1 is concerned with different types of cutting-plane methods for (mixed-integer) linear programs. In Chapter 2 we present a combinatorial algorithm to solve a particular family of unconstrained binary quadratic programs in polynomial time. General unconstrained quadratic binary programs are then considered in Chapter 3, for which we show how information related to the spectrum of the matrix defining the objective may be used to derive bounds on the optimal objective value.In the second part, we present our contributions w.r.t. several classical combinatorial optimization problems. They namely contain studies on descriptions of polytopes related to the maximum cut problem when the sizes of the shores are fixed (Chapter 4). Given an edge weighted graph, this problem consists in identifying a node subset S of prescribed size, such that the sum of the weights of the edges having exactly one endpoint in S is maximized. Another very classical problem in combinatorial optimization is the one which consists in identifying a minimum cardinality dominating set. Recall that given a graph, a dominating set is a node subset S such that each node not in S has at least one neighbor in S. Polyhedral investigations have been carried out w.r.t. the weighted version of the problem and for different generalizations of the domination concept (Chapter 5). A graph partitioning problem called the k-separator problem is then dealt with from different perspectives (complexity, approximations and polyhedral descriptions) in Chapter 6. Basically it consists in identifying a node subset in a graph whose removal induces a graph having connected components of bounded size. Finally, in Chapter 7, we present several features of an original orientation problem in graphs, including the identification of polynomial time solvable cases, several formulations and connections with the maximum cut problem.

Cited by 0

Optimization: a Journal of Mathematical Programming and Operations Research

RWTH Publications (RWTH Aachen) · 2011

Optimization publishes refereed, theoretical and applied papers on the latest developments in fields such as linear, nonlinear, stochastic, parametric, discrete and dynamic programming, control theory and game theory.
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\nA special section is devoted to review papers on theory and methods in interesting areas of mathematical programming and optimization techniques. The journal also publishes conference proceedings, book reviews and announcements.

Cited by 0

Optimization: a Journal of Mathematical Programming and Operations Research

Juan Enrique Martínez-Legaz, Stephan Dempe, V. F. Demyanov et al. · 2011

Optimization publishes refereed, theoretical and applied papers on the latest developments in fields such as linear, nonlinear, stochastic, parametric, discrete and dynamic programming, control theory and game theory. A special section is devoted to review papers on theory and methods in interesting areas of mathematical programming and optimization techniques. The journal also publishes conference proceedings, book reviews and announcements.

Cited by 6

Optimization: A Journal of Mathematical Programming and Operations Research

NC DOCKS at The University of North Carolina at Greensboro, Suthaharan, Shanmugatha "Shan" · NC Digital Online Collection of Knowledge and Scholarship (The University of North Carolina at Greensboro) · 2014

In this article we study support vector machine (SVM) classifiers in the face of uncertain knowledge sets and show how data uncertainty in knowledge sets can be treated in SVM classification by employing robust optimization. We present knowledge-based SVM classifiers with uncertain knowledge sets using convex quadratic optimization duality. We show that the knowledge-based SVM, where prior knowledge is in the form of uncertain linear constraints, results in an uncertain convex optimization problem with a set containment constraint. Using a new extension of Farkas' lemma, we reformulate the robust counterpart of the uncertain convex optimization problem in the case of interval uncertainty as a convex quadratic optimization problem. We then reformulate the resulting convex optimization problems as a simple quadratic optimization problem with non-negativity constraints using the Lagrange duality. We obtain the solution of the converted problem by a fixed point iterative algorithm and establish the convergence of the algorithm. We finally present some preliminary results of our computational experiments of the method

Cited by 0Open access

PROPELLANT OPTIMIZATION PROGRAM FOR COMPUTERS MATHEMATICAL PROCEDURES AND PROGRAMMING.

B. Kubert, L. Sashkin · 1964

Abstract : Modifications to an existing computer program are described, which can determine the composition yielding maximum impulse for multi-compoent propellant mixtures subject to both equality and inequality constraints on the components. The program is coded for up to eight components; the capability extends to ten components. The final report contains the mathematical formulation of the problem and describes the procedures used for the optimization process with the modifications indicated. In addition, instructions for the use of the program and the program flow charts are included. (Author)

Cited by 0

PROPELLANT OPTIMIZATION PROGRAM FOR COMPUTERS MATHEMATICAL PROCEDURES AND PROGRAMMING.

Buley,E.R., Piper,D.G., Kubert,B. et al. · Defense Technical Information Center (DTIC) · 1964

Modifications to an existing computer program are described, which can determine the composition yielding maximum impulse for multi-compoent propellant mixtures subject to both equality and inequality constraints on the components. The program is coded for up to eight components; the capability extends to ten components. The final report contains the mathematical formulation of the problem and describes the procedures used for the optimization process with the modifications indicated. In addition, instructions for the use of the program and the program flow charts are included. (Author)

Cited by 0

Integrating packing and distribution problems and optimization through mathematical programming

Fábio Miguel, Mariano Frutos, Fernando Tohmé et al. · Decision Science Letters · 2015

This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP) problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), which is a variant of the Travelling Salesman Problem (again a NP-Hard problem) with extra constraints. Here we model those two problems in a single framework and use an evolutionary meta-heuristics to solve them jointly. Furthermore, we use data from a real world company as a test-bed for the method introduced here.

Cited by 2Open access

Structural Optimization Using the Design of Experiments and Mathematical Programming.

Takayoshi Kashiwamura, Masaki SHIRATORI, Qiang Yu et al. · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A · 1996

The authors proposed a new practical optimum design method that consists of two steps: the design of experiments and mathematical programming. The design of experiments is used to generate approximate evaluation functions for the controlling behavior depending on the changes in design variables of an object structure, by a series of finite element analyses (FEA). Based upon an orthogonal array of a combination of design variables, effects of the design variables can be calculated by a relatively small number of FEA, and then the approximate evaluation functions are generated by those effects based upon analysis of variance. The evaluation functions can also be used as direct tools for estimating the behavior of design structure. Finally, a successive quadratic programming (SQP) method is employed to solve the optimization problem of the approximate evaluation functions. It is confirmed that the proposed method can be used for almost all kinds of the nonlinear problems including the impact behavior of structures, and that it can be carried out in much smaller number of FEA than the other existing methods. As an example, the present method was used to solve an optimum design problem of an automobile seat frame subjected to impact loading. It was found that the present method is a very effective and powerful tool for the optimum design of various practical design problems.

Cited by 15Open access