General Quadratic Programming and Its Applications in Response Surface Analysis

Enkhbat, Rentsen; Bazarsad, Yadam

doi:10.1007/978-0-387-89496-6_6

Cited by 3 publications

(11 citation statements)

References 5 publications

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“…In Enkhbat and Bazarsad (2010), an algorithm for solving the box-constrained concave quadratic minimization problem is proposed. The first-order approximation set is constructed with n + 1 vectors y j = z + γ j h j , j = 1, .…”

Section: Optimality Conditionsmentioning

confidence: 99%

“…Otherwise, we must apply an iterative algorithm for finding an approximate global solution. Many algorithms have been developed for solving this problem, such as cutting plane methods and partition of feasible domain techniques (Tuy 1964) which do not ensure convergence in certain cases (Zwart 1973), successive underestimating method (Hoffman 1975), branch and bound methods Chen and Burer 2012), combination of branch and bound techniques with cutting plane methods (Thoai and Tuy 1980), approximation sets and Linear Programming (LP) approach (Enkhbat 2003;Chinchuluun et al 2005;Enkhbat and Bazarsad 2010;Bayartugs et al 2014), DC programming approaches (An and Tao 1998;Tuy 2016), techniques which transform the problem to an equivalent integer LP problem (Xia et al 2018), etc.…”

Section: Introductionmentioning

confidence: 99%

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A successive linear approximation algorithm for the global minimization of a concave quadratic program

2020

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In this work, we propose an algorithm for finding an approximate global minimum of a concave quadratic function with a negative semi-definite matrix, subject to linear equality and inequality constraints, where the variables are bounded with finite or infinite bounds. The proposed algorithm starts with an initial extreme point, then it moves from the current extreme point to a new one with a better objective function value. The passage from one basic feasible solution to a new one is done by the construction of certain approximation sets and solving a sequence of linear programming problems. In order to compare our algorithm with the existing approaches, we have developed an implementation with MATLAB and conducted numerical experiments on numerous collections of test problems. The obtained numerical results show the accuracy and the efficiency of our approach.

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Section: Optimality Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A successive linear approximation algorithm for the global minimization of a concave quadratic program

2020

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“…The technological requirements for the variables are given by the box constraints: It can be readily seen that the matrix A 1 is asymmetrical with the eigenvalues λ 1 1,2 = 0.27 ± 5.46i, λ 1 3 = −0.63, λ 1 4 = 0.59, λ 1 5 = −0.01, λ 1 6,7 = 0.02 ± 0.11i, therefore A 1 is an indefinite matrix.…”

Section: Compute the Hessian Of The Function φ(•)mentioning

confidence: 99%

“…, n, are assumed to be found by solving an identification problem for a chosen design of the experiment, for example, the orthogonal central composite design [8]. It is required to find the global extremum of the function f (•) over an experimental region or to equivalently reduce the problem to the indefinite quadratic programming over a box constraint [1,2].…”

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confidence: 99%

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D.C. programming approach for solving an applied ore-processing problem

Enkhbat¹,

Gruzdeva²,

Barkova³

2018

Journal of Industrial &Amp; Management Optimization

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This paper was motivated by a practical optimization problem formulated at the Erdenet Mining Corporation (Mongolia). By solving an identification problem for a chosen design of experiment we developed a quadratic model that quite adequately represents the experimental data. The problem obtained turned out to be the indefinite quadratic program, which we solved by applying the global search theory for a d.c. programming developed by A.S. Strekalovsky [13]-[15]. According to this d.c. optimization theory, we performed a local search that takes into account the structure of the problem in question, and constructed procedures of escaping critical points provided by the local search. The algorithms proposed for d.c. programming were verified using a set of test problems as well as a copper content maximization problem arising at the mining factory.

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New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming

2021

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In this work, we propose a new approach called "Successive Linear Programming Algorithm (SLPA)" for finding an approximate global minimizer of general nonconvex quadratic programs. This algorithm can be initialized by any extreme point of the convex polyhedron of the feasible domain. Furthermore, we generalize the simplex algorithm for finding a local minimizer of concave quadratic programs written in standard form. We prove a new necessary and sufficient condition for local optimality, then we describe the Revised Primal Simplex Algorithm (RPSA). Finally, we propose a hybrid local-global algorithm called "SLPLEX", which combines RPSA with SLPA for solving general concave quadratic programs. In order to compare the proposed algorithms to the branch-and-bound algorithm of CPLEX12.8 and the branch-and-cut algorithm of Quadproga, we develop an implementation with MATLAB and we present numerical experiments on 139 nonconvex quadratic test problems. KeywordsNonconvex quadratic programming • Concave quadratic programming • Successive linear programming • Simplex algorithm • Extreme point • Local minimizer • Global minimizer • Approximate global minimizer • Numerical experiments Mathematics Subject Classification 90C20 • 90C26 • 90C59 B Mohand Bentobache

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General Quadratic Programming and Its Applications in Response Surface Analysis

Cited by 3 publications

References 5 publications

A successive linear approximation algorithm for the global minimization of a concave quadratic program

A successive linear approximation algorithm for the global minimization of a concave quadratic program

D.C. programming approach for solving an applied ore-processing problem

New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming

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