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

✍ Scribed by Soon-Yi Wu; S.-C. Fang

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 541 KB
• Volume: 38
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(99)00203-5

✦ Synopsis

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. (~) 1999 Elsevier Science Ltd. All rights reserved.

Keywords--Convex

semi-infinite programming, Cutting plane method, Duality theory.