A smooth penalty function algorithm for network-structured problems

Article Abstract:

An algorithm for solving large-scale linear programming-optimization problems with embedded network structures is developed. It employs a linear-quadratic penalty function to remove non-network restrictions. This leads to a differentiable and non-separable formulation of the problem which, when subjected to decomposition, results in a series of linear network problems. Its application on multicommodity network flow problems is also discussed.

Operations research, Management science, Mathematical optimization, Optimization theory, Nonlinear programming

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Continuation method for nonlinear complementarity problems via normal maps

Article Abstract:

A study was conducted to analyze the use of smoothing functions to determine the normal map formulation of nonlinear complementarity problems. The characteristics of the smoothing function were examined based on the density functions determining the smooth approximations. The structure of the subproblems resulting from the proposed continuation method was then examined for various choices of smoothing functions.

Analysis, Linear complementarity problem, Continuation methods

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A simple duality proof in convex quadratic programming with a quadratic constraint, and some applications

Article Abstract:

A simple derivation of duality for convex quadratic programs is presented.

Usage, Duality theory (Mathematics), Quadratic programming

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