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Low Rank Nonconvex Quadratic Programming
1997Quadratic programming (QP) problems, namely minimization of quadratic functions under linear constraints, have been under extensive research since the early days of mathematical programming. In particular, if the objective function is convex, then a large scale problem can be solved by several simplex type algorithms(Beale (1959), Cottle, Dantzig (1968)
Hiroshi Konno +2 more
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Nonconvex Quadratic Programming
1998Nonconvex quadratic programming deals with optimization problems described by means of linear and quadratic functions, i.e., functions with lowest degree of nonconvexity. One of the earliest significant results in this area is the celebrated S-Lemma of Yakubovich which plays a major role in the development of quadratic optimization.
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Algorithms for parametric nonconvex programming
Journal of Optimization Theory and Applications, 1982In this paper, we consider a general family of nonconvex programming problems. All of the objective functions of the problems in this family are identical, but their feasibility regions depend upon a parameter ϑ. This family of problems is called a parametric nonconvex program (PNP).
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Nonconvex Structures in Nonlinear Programming
Operations Research, 2004Nonsmoothness and nonconvexity in optimization problems often arise because a combinatorial structure is imposed on smooth or convex data. The combinatorial aspect can be explicit, e.g., through the use of “max,” “min,” or “if” statements in a model; or implicit, as in the case of bilevel optimization, where the combinatorial structure arises from the
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An Interior Method for Nonconvex Semidefinite Programs
Optimization and Engineering, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An Interior-Point Algorithm for Nonconvex Nonlinear Programming
Computational Optimization and Applications, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vanderbei, Robert J., Shanno, David F.
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Global Minimization in Nonconvex All-Quadratic Programming
Management Science, 1975This paper describes a branch and bound algorithm for the global minimization of a quadratic objective function subject to quadratic constraints over a bounded interval. No assumptions are made regarding the convexity of either the objective or the constraints. The algorithm consists of three basic steps. First, a local minimum is identified. Next, an
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Quality in Mixed Integer Nonconvex and Nondifferentiable Programming
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1979AbstractIn this paper we formulate the duals of linear and nonlinear fractional programs and certain nondifferentiable programs in which some variables are integer constrained. We also show that in one of the cases an algorithm can be developed as an immediate consequence of this duality theory.
Chandra, Suresh, Chandramohan, M.
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Efficiency and Solution Approaches to Bicriteria Nonconvex Programs
Journal of Global Optimization, 1997The authors consider bicriteria optimization problems in finite dimensions. Based on the known \(\varepsilon\)-constranit auxiliary problem and a special augmented Lagrangian a scalarization technique is presented. The concepts of \(q_i\)-approachable points and a so-called augmented duality gap are proposed.
Tenhuisen, Matthew L. +1 more
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