TD-01: Sparse and Large-Scale Optimization
Stream: Sparse and Large-Scale Optimization
Room: Fermat
Chair(s):
Emmanuel Soubies
On nondegenerate M-stationary points for mathematical programs with sparsity constraint
Sebastian Lämmel
We study mathematical programs with sparsity constraint (MPSC) from a topological point of view. Special focus will be on M-stationary points from Burdakov et al. (2016). We introduce nondegenerate M-stationary points, define their M-index, and show that all M-stationary points are generically nondegenerate. In particular, the sparsity constraint is active at all local minimizers of a generic MPSC. Moreover, we discuss the issues of instability and degeneracy of points due to different stationarity concepts.
AAR-Based Decomposition Method For Limit Analysis
Nima Rabiei, Ali Almisreb
A method is suggested for decomposing a class of non-linear convex programmes which are encountered in limit analysis. These problems have second-order conic constraints and a single complicating variable in the objective function. The method is based on finding the distance between the feasible sets of the decomposed problems, and updating the global optimal value according to the value of this distance. The latter is found by exploiting the method of Averaged Alternating Reflections which is here adapted to the optimization problem at hand.
Expanding Boundaries of Gap Safe Screening
Cassio Dantas, Emmanuel Soubies, Cédric Févotte
Safe screening techniques allow the early elimination of zero coordinates in the solution of sparse optimization problems. In this work, we extend the existing Gap Safe screening framework by relaxing the global strong-concavity assumption on the dual cost function. Local regularity properties are considered instead. Besides extending safe screening to a broader class of functions that includes beta-divergences (e.g., the Kullback-Leibler divergence), the proposed approach also improves upon the existing Gap Safe screening rules on previously applicable cases (e.g., logistic regression).