Journal ArticleDOI
Convergent Algorithms for Minimizing a Concave Function
Nguyen Van Thoai,Hoang Tuy +1 more
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A class of convergent algorithms is proposed, which is based upon a combination of the branch and bound technique with the cutting method developed earlier by H. Tuy, for the problem of minimizing a concave function over a polytope.Abstract:
For the problem of minimizing a concave function over a polytope a class of convergent algorithms is proposed, which is based upon a combination of the branch and bound technique with the cutting method developed earlier by H. Tuy.read more
Citations
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DC programming: overview
Reiner Horst,Nguyen Van Thoai +1 more
TL;DR: The purpose of this overview is to discuss main theoretical results, some applications, and solution methods for this interesting and important class of programming problems.
Journal ArticleDOI
Variations and extension of the convex–concave procedure
Thomas Lipp,Stephen Boyd +1 more
TL;DR: This work investigates the convex–concave procedure, a local heuristic that utilizes the tools of convex optimization to find local optima of difference of conveX (DC) programming problems, and generalizes the algorithm to include vector inequalities.
Journal ArticleDOI
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
On the design of maximally sparse beamforming arrays
Richard M. Leahy,Brian D. Jeffs +1 more
TL;DR: In this article, the problem of designing nonuniformly spaced arrays is formulated as one of constrained optimization in which the cost function is chosen to select the array with the minimum number of elements.
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.
References
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Journal ArticleDOI
Intersection Cuts—A New Type of Cutting Planes for Integer Programming
TL;DR: The paper gives a simple formula for finding the equation of the hyperplane, discusses some ways of strengthening the cut, proposes an algorithm, and gives a finiteness proof.
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Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems
TL;DR: A broad class of problems can be formulated as minimizing a concave function over the solution set of a Leontief substitution system, which includes deterministic single- and multi-facility economic lot size, lot-size smoothing, warehousing, product-assortment, batch-queuing, capacity-expansion, investment consumption, and reservoir-control problems with concave cost functions.
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A cutting plane algorithm for solving bilinear programs
TL;DR: A cutting plane algorithm is proposed to solve a special class of nonconvex quadratic program referred to as a bilinear program in the literature and the preliminary results of numerical experiments are encouraging.
Journal ArticleDOI
A Deterministic Multiproduct, Multi-Facility Production and Inventory Model
TL;DR: A deterministic multiproduct, multifacility, multiperiod production planning model, which considers concave production costs, which can depend upon the production in several different facilities, and piecewise concave inventory costs.
Journal ArticleDOI
A Successive Underestimation Method for Concave Minimization Problems
James E. Falk,Karla R. Hoffman +1 more
TL;DR: A new method designed to globally minimize concave functions over linear polyhedra is described, and an example problem is solved, and computational considerations are discussed.