553. On global optimization of some nonlinear problems involving disjunctive constraints
Invited abstract in session TB-4: Stochastic and Deterministic Global Optimization, stream Global optimization.
Tuesday, 10:30-12:30Room: B100/5013
Authors (first author is the speaker)
| 1. | Sonia Cafieri
|
| ENAC - Ecole Nationale d'Aviation Civile | |
| 2. | Marcel Mongeau
|
| ENAC | |
| 3. | Sebastien Bourguignon
|
| Ecole Centrale de Nantes | |
| 4. | Gwenaël Samain
|
| LS2N |
Abstract
We propose Branch-and-Bound-based optimization methods for some nonlinear problems whose only combinatorial aspect comes from their disjunctive constraints. We build on the recently introduced continuous quadrant penalty formulation of disjunctive constraints, which constitutes a continuous-optimization alternative to the classical formulations (such as the bigM formulation) based on the introduction of binary variables. Such a formulation, based on the introduction of a smooth piecewice-quadratic penalty function, yields to a continuous nonconvex problem. The solution of this problem allows an efficient computation of upper bounds to be used within Branch-and-Bound.
We apply the proposed approach to a problem from discrete geometry, where a rectangle has to be covered by minimal-radius disks, and to a problem from compressed sensing, where a sparsity-enhancing cardinality-constrained inverse problem in signal processing is addressed.
Keywords
- Global optimization
- Nonlinear mixed integer optimization
- Applications of continuous optimization
Status: accepted
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