NEW PARTITIONING METHOD FOR A CLASS OF NONCONVEX OPTIMIZATION PROBLEMS

• 成果类型: Article
• 署名作者: THACH, PT
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.17.1.43
• 发表日期: 1992
• 页码: 43-60
• 关键词: cutting plane algorithms; constraints

摘要

We consider the problem min{f(x, y): g(i)(x, y) less-than-or-equal-to 0, i = 1,..., m, x is-an-element-of X, y is-an-element-of Y} where f and the g(i) are lower semicontinuous and convex in y for fixed x but not convex jointly in (x, y), X is a compact subset of R(n), Y is a closed convex set in R(m). In order to decompose this problem into subproblems, each depending either on the x-variables alone or the y-variables alone, we propose a new partitioning method which does not require the Benders-Geoffrion's condition on the structure of joint constraints and the objective function. The relaxed master problems generated by our partitioning method are d.c. programs and they can be systematically solved by recent algorithms.