127. Genericity and stability in linear conic programming
Invited abstract in session TC-3: In memory of Georg Still - part 2, stream In memory of Georg Still.
Thursday, 11:25 - 12:40Room: M:J
Authors (first author is the speaker)
| 1. | Bolor Jargalsaikhan
|
| 2. | Mirjam Duer
|
| Augsburg University | |
| 3. | Georg Still
|
| Mathematics, University of Twente |
Abstract
In linear conic programming, we maximize or minimize a linear function over the intersection of an affine space and a convex cone. In this talk, we discuss properties of conic problems such as uniqueness of the optimal solution, nondegeneracy, and strict complementarity. A property is said to be stable at a problem instance if the property still holds under a small perturbation of the problem data. We say that a property is weakly generic if the property holds for almost all problem instances. We start by showing that Slater’s condition is weakly generic and stable. It is known that uniqueness of the optimal solution, nondegeneracy, strict complementarity are weakly generic properties in conic programming, so we study the stability of these weakly generic properties. For the semidefinite programs, we show that all these properties are stable. Moreover, we characterize first order optimal solutions in conic programs and give necessary and sufficient conditions for their stability.
Keywords
- Conic and semidefinite optimization
- Semi-infinite optimization
Status: accepted
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