On the strong concavity of the dual function of an optimization problem

2020/06/27 by Vincent Guigues, Guigues, Vincent
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2006.16781

openalex publication_date 2020/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide three new proofs of the strong concavity of the dual function of some convex optimization problems. For problems with nonlinear constraints, we show that the the assumption of strong convexity of the objective cannot be weakened to convexity and that the assumption that the gradients of all constraints at the optimal solution are linearly independent cannot be further weakened. Finally, we illustrate our results with several examples.

Citations

• Quelques propriétés des opérateurs angle-bornés etn-cycliquement monotones

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