Journal article
A Central Cutting Plane Algorithm for Convex Semi-Infinite Programming Problems
SIAM journal on optimization, Vol.3(4), pp.901-918
11/01/1993
DOI: 10.1137/0803047
Abstract
The central cutting plane algorithm for linear semi-infinite programming (SIP) is extended to nonlinear convex SIP of the form min $\{ f ( x )|x \in H,g ( x,t ) \leq 0\,{\text{all}}\,t \in S \}$. Under differentiability assumptions that are weaker than those employed in superlinearly convergent algorithms, a linear convergence rate is established that has additional important features. These features are the ability to (i) generate a cut from any violated constraint; (ii) invoke efficient constraint-dropping rules for management of linear programming (LP) subproblem size; (iii) provide an efficient grid management scheme to generate cuts and ultimately to test feasibility to a high degree of accuracy, as well as to provide an automatic grid refinement for use in obtaining admissible starting solutions for the nonlinear system of first-order conditions; and, (iv) provide primal and dual (Lagrangian) SIP feasible solutions in a finite number of iterations. Numerical tests are provided on a collection of problems that have appeared in the literature including some moderately sized problems from complex approximation theory.
Details
- Title: Subtitle
- A Central Cutting Plane Algorithm for Convex Semi-Infinite Programming Problems
- Creators
- K. O KortanekHoon No
- Resource Type
- Journal article
- Publication Details
- SIAM journal on optimization, Vol.3(4), pp.901-918
- DOI
- 10.1137/0803047
- ISSN
- 1052-6234
- eISSN
- 1095-7189
- Publisher
- Society for Industrial and Applied Mathematics
- Language
- English
- Date published
- 11/01/1993
- Academic Unit
- Business Analytics
- Record Identifier
- 9984963085302771
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