98. Lagrange duality on DC evenly convex optimization problems via a generalized conjugation scheme
Invited abstract in session TD-3: Variational techniques and subdifferentials, stream Variational analysis: theory and algorithms.
Thursday, 14:10 - 15:50Room: M:J
Authors (first author is the speaker)
| 1. | Maria Dolores Fajardo
|
| Mathematics, University Of Alicante | |
| 2. | Jose Vidal-Nunez
|
| University of Alcalá |
Abstract
In this talk, we present how Lagrange duality is connected to optimization problems whose objective function is the difference of two convex functions, briefly called DC problems. We enter two Lagrange dual problems, each of them obtained via a different approach. While one of the duals corresponds to the standard formulation of the Lagrange dual problem, the other is written in terms of conjugate functions. When one of the involved functions in the objective is evenly convex, both problems are equivalent, but this relation is no longer true in the general setting. For this reason, we show conditions ensuring not only weak, but also zero duality and strong duality between the primal and one of the dual problems written using conjugate functions. For the other dual, and due to the fact that weak duality holds by construction, we just develop conditions for zero duality gap and strong duality between the primal DC problem and its (standard) Lagrange dual problem. We apply also the obtained results to characterize weak and strong duality together with zero duality gap between the primal problem and its Fenchel-Lagrange dual.
Keywords
- Semi-infinite optimization
Status: accepted
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