Linearly constrained global optimization via piecewise-linear approximation

Authors:
Hao Zhang;Shuning Wang
Affiliations:
Department of Automation, Tsinghua University, Beijing 100084, PR China;Department of Automation, Tsinghua University, Beijing 100084, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 5
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Abstract

This paper considers the problem of optimizing a continuous nonlinear objective function subject to linear constraints via a piecewise-linear approximation. A systematic approach is proposed, which uses a lattice piecewise-linear model to approximate the nonlinear objective function on a simplicial partition and determines an approximately globally optimal solution by solving a set of standard linear programs. The new approach is applicable to any continuous objective function rather than to separable ones only and could be useful to treat more complex nonlinear problems. A numerical example is given to illustrate the practicability.