Application of convex sampling in optimization
The optimization problem of minimizing a linear objective function over a general convex body known only by a weak membership test is a central problem in convex optimization. Traditional methods require the (expensive) construction of separating relations (cuts) or gradient information (which is often not available). We propose to demonstrate how a near uniform convex body sampler can be used as the central routine in an effective randomized polynomial time algorithm for approximately minimizing a linear objective function over an up-monotone convex set presented by a membership oracle. The sampling technique has been developed by Diaconis, Dyer, Frieze, Kannan, Lovasz, Simonovits and others. Application to general optimization has been proposed by Faigle and Gademann. The primary contribution outlined here is work with Kannan and Tayur attempting to establish fast specialized algorithms for up-monotone convex bodies.
- OSTI ID:
- 36308
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
Similar Records
Generalized convexity and global optimization
Polynomial methods for separable convex optimization in unimodular spaces