Solving convex programs with infinitely many linear constraints by a relaxed cutting plane method

Solving convex programs with infinitely many linear constraints by a relaxed cutting plane method

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Article ID: iaor20003027
Country: United Kingdom
Volume: 38
Issue: 3/4
Start Page Number: 23
End Page Number: 33
Publication Date: Aug 1999
Journal: Computers & Mathematics with Applications
Authors: ,
Abstract:

One of the major computational bottlenecks of using the conventional cutting plane approach to solve convex programming problems with infinitely many linear constraints lies in finding a global optimizer of a nonlinear and nonconvex program. This paper presents a relaxed scheme to generate a new cut. In each iteration, the proposed scheme chooses a point at which the constraints are violated to a degree rather than at which the violation is maximized. A convergence proof is provided. The proposed scheme also exhibits the capability of generating an approximate solution to any level of accuracy in a finite number of iterations.

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