Search results for " 49M27"

showing 3 items of 3 documents

An Adaptive Alternating Direction Method of Multipliers

2021

AbstractThe alternating direction method of multipliers (ADMM) is a powerful splitting algorithm for linearly constrained convex optimization problems. In view of its popularity and applicability, a growing attention is drawn toward the ADMM in nonconvex settings. Recent studies of minimization problems for nonconvex functions include various combinations of assumptions on the objective function including, in particular, a Lipschitz gradient assumption. We consider the case where the objective is the sum of a strongly convex function and a weakly convex function. To this end, we present and study an adaptive version of the ADMM which incorporates generalized notions of convexity and penalty…

Control and Optimizationsignal denoisingApplied Mathematicsalternating direction method of multipliersMathematics::Optimization and Controldouglas–rachford algorithmUNESCO::CIENCIAS TECNOLÓGICASManagement Science and Operations Researchcomonotonicityweakly convex functionOptimization and Control (math.OC)47H05 47N10 47J25 49M27 65K15FOS: Mathematicsfirm thresholdingMathematics - Optimization and Control
researchProduct

Regularity of sets under a reformulation in a product space of reduced dimension

2023

Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility problems defined by finitely many sets, some other require the use of a product space reformulation to construct equivalent problems with two sets. In this work we analyze how some regularity properties are preserved under a reformulation in a product space of reduced dimension. This allows us to establish local linear convergence of parallel projection methods which are constructed through this reformulation.

Optimization and Control (math.OC)FOS: Mathematics47H05 47J25 49M27 65K10 90C30Mathematics - Optimization and Control
researchProduct

A product space reformulation with reduced dimension for splitting algorithms

2021

AbstractIn this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra’s classical reformulation with a different decomposition, which results in a reduction of the dimension of the outcoming product Hilbert space. We discuss the case of not necessarily convex feasibility and best approximation problems. By applying existing splitting methods to the proposed reformulation we obtain new parallel variants of them with a reduction in the number of variables. The convergence of the new algorithms is straightforwardly derived with no further assump…

Control and OptimizationApplied Mathematicsdouglas – rachford algorithm47H05 47J25 49M27 65K10 90C30UNESCO::CIENCIAS TECNOLÓGICASComputational MathematicsOptimization and Control (math.OC)splitting algorithmprojection methodsFOS: Mathematicspierra’s product space reformulationmonotone inclusionsMathematics - Optimization and Controlfeasibility problemComputational Optimization and Applications
researchProduct