SIAM Journal on Optimization, Volume 34, Issue 2, Page 1646-1678, June 2024. Abstract. We consider a class of convex optimization problems in a Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those established for the linear programming setting in...

SIAM Journal on Optimization, Volume 34, Issue 2, Page 1622-1645, June 2024. Abstract. Augmented Lagrangian dual augments the classical Lagrangian dual with a nonnegative nonlinear penalty function of the violation of the relaxed/dualized constraints in order to reduce the duality gap. We investigate the cases in which mixed integer convex optimization...

SIAM Journal on Optimization, Volume 34, Issue 2, Page 1595-1621, June 2024. Abstract. We investigate frugal splitting operators for finite sum monotone inclusion problems. These operators utilize exactly one direct or resolvent evaluation of each operator of the sum, and the splitting operator’s output is dictated by linear combinations of these evaluations’...

SIAM Journal on Optimization, Volume 34, Issue 2, Page 1569-1594, June 2024. Abstract. In this paper, we propose several graph-based extensions of the Douglas–Rachford splitting (DRS) method to solve monotone inclusion problems involving the sum of [math] maximal monotone operators. Our construction is based on the choice of two nested graphs, to...

SIAM Journal on Optimization, Volume 34, Issue 2, Page 1540-1568, June 2024. Abstract. We introduce a family of [math]-rectangular robust Markov decision processes ([math]-RMDPs) indexed with [math]. In each state, the ambiguity set of transition probability mass functions (pmfs) across actions equals a sublevel set of the [math]-norm of a vector...

SIAM Journal on Optimization, Volume 34, Issue 2, Page 1515-1539, June 2024. Abstract. The Fritz John (FJ) and Karush–Kuhn–Tucker (KKT) conditions are fundamental tools for characterizing minimizers and form the basis of almost all methods for constrained optimization. Since the seminal works of Fritz John, Karush, Kuhn, and Tucker, FJ/KKT conditions...