Global optimization of separable objective functions on convex polyhedra via piecewise-linear approximation

Authors:
Hao Zhang;Shuning Wang
Affiliations:
Department of Automation, Tsinghua University, Beijing, PR China;Department of Automation, Tsinghua University, Beijing, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 2
Cited 1

Approximating separable nonlinear functions via mixed zero-one programs

Operations Research Letters
On mixed-integer zero-one representations for separable lower-semicontinuous piecewise-linear functions

Operations Research Letters

Linearly constrained global optimization via piecewise-linear approximation

Journal of Computational and Applied Mathematics

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Abstract

The problem of minimizing a separable nonlinear objective function under linear constraints is considered in this paper. A systematic approach is proposed to obtain an approximately globally optimal solution via piecewise-linear approximation. By means of the new approach a minimum point of the original problem confined in a region where more than one linear piece is needed for satisfactory approximation can be found by solving only one linear programming problem. Hence, the number of linear programming problems to be solved for finding the approximately globally optimal solution may be much less than that of the regions partitioned. In addition, zero-one variables are not introduced in this approach. These features are desirable for efficient computation. The practicability of the approach is demonstrated by an example.