In this note we focus on a comparison of two eecient methods to solve quadratic constrained optimal control problems governed by elliptic partial-diierential equations. One of them is based on a generalized Moreau-Yosida formulation of the constrained optimal control problem which results in an active set strategy involving primal and dual variables. The second approach is based on interior poi...

We consider a nonlinear Neumann elliptic inclusion with a source (reaction term) consisting of a convex subdifferential plus a multivalued term depending on the gradient. The convex subdifferential incorporates in our framework problems with unilateral constraints (variational inequalities). Using topological methods and the Moreau-Yosida approximations of the subdifferential term, we establish...

In this paper we provide implementable methods for solving nondifferentiable convex optimization problems. A typical method minimizes an approximate Moreau–Yosida regularization using a quasi-Newton technique with inexact function and gradient values which are generated by a finite inner bundle algorithm. For a BFGS bundle-type method global and superlinear convergence results for the outer ite...

A new generalized Yosida inclusion problem, involving A-relaxed co-accretive mapping, is introduced. The resolvent and associated approximation operator construed a few of its characteristics are discussed. existence result quantified in q-uniformly smooth Banach spaces. four-step iterative scheme proposed convergence analysis Our theoretical assertions illustrated by numerical example. In addi...

We describe a semigroup of abstract semilinear functional differential equations with infinite delay by the use of the Crandall Liggett theorem. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. We clarify the properties of the phase space ensuring equivalence between the equation under investigation and the non...

The classical degree function constructed earlier for pseudomonotone mappings has been used to develop a broader degree theory of classical type for the sum of a maximal monotone map from a reflexive Banach space to its dual together with a bounded pseudomonotone map. The proof uses the generalized Yosida approximation of the maximal monotone mapping.

State constrained optimal control problems represent severe analytical and numerical challenges. A numerical algorithm based on an active set strategy involving primal as well as dual variables, suggested by a generalized Moreau-Yosida regularization of the state constraint is proposed and analyzed. Numerical examples are included.

Maximally monotone operators are fundamental objects in modern optimization. The main classes of subdifferential and matrices with a positive semidefinite symmetric part. In this paper, we study nice class operators: displacement mappings isometries finite order. We derive explicit formulas for resolvents, Yosida approximations, (set-valued Moore-Penrose) inverses. illustrate our results by con...