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- Title
A MODIFICATION PIECEWISE CONVEXIFICATION METHOD WITH A CLASSIFICATION STRATEGY FOR BOX-CONSTRAINED NON-CONVEX OPTIMIZATION PROGRAMS.
- Authors
QIAO ZHU; LIPING TANG; XINMIN YANG
- Abstract
This paper presents a piecewise convexification method with a box classification strategy to approximate the entire globally optimal solution set of non-convex optimization problems with box constraints. First, the box classification strategy is proposed based on the convexity of the objective function on the sub-boxes, which helps to reduce the number of box divisions and improve the computational efficiency. At the same time, we construct the piecewise convexification problem of the original non-convex optimization problem by applying the α-based Branch-and-Bound (a BB) method, and we define the (approximate) solution set of the piecewise convexification problem based on the result of classifying the sub-boxes. Then, it is deduced that the globally optimal solution set can be approximated by the (approximate) solution set of the piecewise convexification problem. Finally, a piecewise convexification algorithm is proposed that includes a new subset selection technique for division and two new termination tests. The results of our experiments demonstrate the effectiveness and general superiority of our approach over the competition.
- Subjects
NONCONVEX programming; MATHEMATICAL optimization; MATHEMATICAL formulas; MATHEMATICAL analysis; COMPUTER algorithms
- Publication
Journal of Nonlinear & Variational Analysis, 2024, Vol 8, Issue 1, p125
- ISSN
2560-6921
- Publication type
Article
- DOI
10.23952/jnva.8.2024.1.07