Abstract
We consider linear optimization over a nonempty convex semialgebraic feasible region F . Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique "active" manifold, around which F is "partly smooth," and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F. © 2011 INFORMS.
Original language | English |
---|---|
Pages (from-to) | 55-70 |
Journal | Mathematics of Operations Research |
Volume | 36 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Feb 2011 |
Keywords
- Active sets
- Convex optimization
- Generic
- Identifiable surface
- Partial smoothness
- Second-order sufficient conditions
- Semialgebraic
- Sensitivity analysis