Journal of Optimization Theory and Applications
Constrained global optimization: algorithms and applications
Constrained global optimization: algorithms and applications
Concave minimization via collapsing polytopes
Operations Research
Journal of Optimization Theory and Applications
Mathematical Programming: Series A and B - Special Issue: Essays on Nonconvex Optimization
On the structure and properties of linear multilevel programming problem
Journal of Optimization Theory and Applications
Concave minimization via conical partitions and polyhedral outer approximation
Mathematical Programming: Series A and B
Ic layout generation and compaction using mathematical optimization
Ic layout generation and compaction using mathematical optimization
Operations Research Letters
Capacity planning in networks of queues with manufacturing applications
Mathematical and Computer Modelling: An International Journal
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This paper presents a new algorithm for globally minimizing a separable, concave function over a compact convex set. The algorithm uses partial outer approximation and branch and bound. The major computational effort required is solving linear programming problems at some nodes of the branch and bound tree, and solving simple univariate minimizations in some iterations. The algorithm partially mitigates the rapid growth in the number of constraints of the linear programs that would frequently occur if traditional outer approximation were used. Furthermore, unlike outer approximation, the algorithm does not explicitly construct polyhedra which contain the feasible region.