New Partitioning Method for a Class of Nonconvex Optimization Problems

We consider the problem min{ f ( x , y ): g i ( x , y ) 0, i = 1, ..., m , x X , y 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 int...

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Bibliographic Details
Published in:Mathematics of operations research 1992-02, Vol.17 (1), p.43-60
Main Author: Thach, Phan Thien
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Approximation
d.c. program
Decomposition methods
Exact sciences and technology
global optimization
Hypersurfaces
Iterative solutions
Mathematical functions
nonconvex decomposition
Operational research and scientific management
Operational research. Management science
Optimal solutions
Optimization. Search problems
partitioning method
Polytopes
Separators
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Summary:We consider the problem min{ f ( x , y ): g i ( x , y ) 0, i = 1, ..., m , x X , y 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.
ISSN:0364-765X
1526-5471
DOI:10.1287/moor.17.1.43