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2313. Generalized convexity applied to branch-and-bound algorithms for MINLPs
Invited abstract in session TC-4: Recent Advances in MINLP, stream MINLP.
Tuesday, 12:30-14:00Room: 1001 (building: 202)
Authors (first author is the speaker)
| 1. | Ksenia Bestuzheva
|
| GAMS Software GmbH |
Abstract
One of the key properties of convex problems is that every stationary point is a global optimum, and nonlinear programming algorithms that converge to local optima are thus guaranteed to find the global optimum. However, some nonconvex problems possess the same property. This observation together with empirical evidence that local search solvers often find global optima of nonconvex problems such as optimal power flow and pooling has motivated research into generalizations of convexity. This presentation proposes a new generalization which we refer to as optima-invexity: the property that only one connected set of optimal solutions exists. We discuss conditions for optima-invexity and its applications within spatial branch-and-bound algorithms for mixed-integer nonlinear programs.
Keywords
- Generalized Convex Optimization
- Branch and Cut
- Global Optimization
Status: accepted
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