Journal ArticleDOI
Global minimization of large-scale constrained concave quadratic problems by separable programming
J. B. Rosen,P M Pardolas +1 more
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The global minimization of a large-scale linearly constrained concave quadratic problem is considered and a guaranteedε-approximate solution is obtained by solving a single liner zero–one mixed integer programming problem.Abstract:
The global minimization of a large-scale linearly constrained concave quadratic problem is considered. The concave quadratic part of the objective function is given in terms of the nonlinear variablesx ∈R
n
, while the linear part is in terms ofy ∈R
k. For large-scale problems we may havek much larger thann. The original problem is reduced to an equivalent separable problem by solving a multiple-cost-row linear program with 2n cost rows. The solution of one additional linear program gives an incumbent vertex which is a candidate for the global minimum, and also gives a bound on the relative error in the function value of this incumbent. Ana priori bound on this relative error is obtained, which is shown to be ≤ 0.25, in important cases. If the incumbent is not a satisfactory approximation to the global minimum, a guaranteede-approximate solution is obtained by solving a single liner zero–one mixed integer programming problem. This integer problem is formulated by a simple piecewise-linear underestimation of the separable problem.read more
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Solving a Class of Linearly Constrained Indefinite QuadraticProblems by D.C. Algorithms
Le Thi Hoai An,Pham Dinh Tao +1 more
TL;DR: The new algorithm, CDA, efficiently produces local optima and sometimes produces global optima inLinearly constrained indefinite quadratic problems and a decomposition branch and bound method for globally solving these problems is proposed.
Journal ArticleDOI
GloMIQO: Global mixed-integer quadratic optimizer
TL;DR: GloMIQO is introduced, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs to $${\varepsilon}$$-global optimality, and its algorithmic components are presented for reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, and finding good feasible solutions.
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Minimum concave-cost network flow problems: applications, complexity, and algorithms
TL;DR: An overview of solution techniques for minimum concave-cost network flow problems is presented, with some new results given regarding the implementation of a particular branch-and-bound approach.
Journal ArticleDOI
Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO
TL;DR: This work provides a comprehensive and detailed literature review in terms of significant theoretical contributions, algorithmic developments, software implementations and applications for both MINLP and CDFO, and shows their individual prerequisites, formulations and applicability.
Journal ArticleDOI
An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds
Panos M. Pardalos,N. Kovoor +1 more
TL;DR: An O(n) algorithm for a singly constrained convex quadratic program using binary search to solve the Kuhn-Tucker system is given.
References
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The Quadratic Assignment Problem
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Matrix Eigensystem Routines - Eispack Guide
TL;DR: Eispack as discussed by the authors is an Eispack subroutine that uses handbook algol procedures to validate and validate EISPACKs and is used for EisPacks.
Journal ArticleDOI
Solving Large-Scale Zero-One Linear Programming Problems
TL;DR: The results indicate that cutting-planes related to the facets of the underlying polytope are an indispensable tool for the exact solution of this class of problem.
Journal ArticleDOI
Methods for global concave minimization: A bibliographic survey
Panos M. Pardalos,J. B. Rosen +1 more
TL;DR: A bibliographic survey of constrained global concave minimization can be found in this paper, where the main ideas in each paper are summarized in a short summary form, including those concerned with large-scale global minimization and bilinear programming.