6 papers
A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Łojasiewicz condition
Felipe Atenas, Alejandro Jofré, Pedro Pérez-Aros +1
This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semico…
Projection, Degeneracy, and Singularity Degree for Spectrahedra
Haesol Im, Woosuk L. Jung, David Torregrosa-Belén +1
Facial reduction, FR, is a regularization technique for convex programs where the strict feasibility constraint qualification, CQ, fails.Though this CQ holds generically, failure i…
Optimal Diagonal Preconditioning Beyond Worst-Case Conditioning: Theory and Practice of Omega Scaling
Saeed Ghadimi, Woosuk L. Jung, Arnesh Sujanani +2
We study optimal diagonal preconditioning using the classical worst-case -condition number and the averaging-based -condition number. For the -optimal preconditioning p…
Nonmonotone subgradient methods based on a local descent lemma
Francisco J. Aragón-Artacho, Rubén Campoy, Pedro Pérez-Aros +1
In this paper we present a nonmonotone line search subgradient algorithm tailored to upper- functions. This is a family of nonsmooth and nonconvex functions that sat…
Randomized block proximal method with locally Lipschitz continuous gradient
Pedro Pérez-Aros, Pedro Pérez-Aros, David Torregrosa-Belén +1
Block-coordinate algorithms are recognized to furnish efficient iterative schemes for addressing large-scale problems, especially when the computation of full derivatives entails s…
The -Condition Number: Applications to Optimal Preconditioning and Low Rank Generalized Jacobian Updating
Woosuk L. Jung, David Torregrosa-Belén, Henry Wolkowicz
Preconditioning is essential in iterative methods for solving linear systems. It is also the implicit objective in updating approximations of Jacobians in optimization methods, e.g…