Genericity Results in Linear Conic Programming-A Tour d'Horizon
| Autor: | Georg Still, Bolor Jargalsaikhan, Mirjam Dür |
|---|---|
| Přispěvatelé: | Discrete Mathematics and Mathematical Programming |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
strict complementarity Slater’s condition Generic property General Mathematics 0211 other engineering and technologies Duality (optimization) 010103 numerical & computational mathematics 02 engineering and technology Management Science and Operations Research uniqueness and nondegeneracy of optimal solutions Slater's condition 01 natural sciences Combinatorics CONVEX-OPTIMIZATION DUALITY Strong duality Uniqueness 0101 mathematics Mathematics 021103 operations research generic properties stability conic optimization n/a OA procedure Computer Science Applications Geometric measure theory Conic section BODIES SEMIINFINITE OPTIMIZATION Conic optimization |
| Zdroj: | Mathematics of Operations Research, 42(1), 77-94. INFORMS Mathematics of operations research, 42(1). INFORMS Institute for Operations Research and the Management Sciences |
| ISSN: | 0364-765X |
| Popis: | This paper is concerned with so-called generic properties of general linear conic programs. Many results have been obtained on this subject during the last two decades. For example, it is known that uniqueness, strict complementarity, and nondegeneracy of optimal solutions hold for almost all problem instances. Strong duality holds generically in a stronger sense, i.e., it holds for a generic subset of problem instances. In this paper, we survey known results and present new ones. In particular we give an easy proof of the fact that Slater’s condition holds generically in linear conic programming. We further discuss the problem of stability of uniqueness, nondegeneracy, and strict complementarity. We also comment on the fact that in general, a conic program cannot be treated as a smooth problem and that techniques from nonsmooth geometric measure theory are needed. |
| Databáze: | OpenAIRE |
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