In this work we give a new criteria for the existence of periodic and almost periodic solutions for some differential equation in a Banach space. The linear part is nondensely defined and satisfies the Hille-Yosida condition. We prove the existence of periodic and almost periodic solutions with condition that is more general than the known exponential dichotomy. We apply the new criteria for th...

The low-energy properties of the Anderson impurity are studied under a finite bias voltage V using the perturbation theory in U of Yamada and Yosida in the nonequilibrium Keldysh diagrammatic formalism. The self-energy is calculated exactly up to terms of order ω, T 2 and V 2 using Ward identities. The coefficients are defined with respect to the equilibrium ground state, and contain all contri...

First a general framework for a hybrid super-relaxed proximal point algorithm based on the notion of H-maximal monotonicity is introduced, and then the convergence analysis for solving a general class of nonlinear inclusion problems is explored. The framework developed in this communication is quite suitable to generalize first-order evolution equations based on the generalized nonlinear Yosida...

In a general Hilbert framework, we consider continuous gradient-like dynamical systems for constrained multiobjective optimization involving non-smooth convex objective functions. Based on the Yosida regularization of the subdifferential operators involved in the system, we obtain the existence of strong global trajectories. We prove a descent property for each objective function, and the conve...

An adjustment scheme for the regularization parameter of a Moreau-Yosida-based regularization, or relaxation, approach to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method utilizes error estimates of an associated finite element discretization of the regularized problems for the optimal selection of the regularization parameter in ...

In this paper, we establish a Hopf bifurcation theorem for abstract Cauchy problems in which the linear operator is not densely defined and is not a Hille–Yosida operator. The theorem is proved using the center manifold theory for nondensely defined Cauchy problems associated with the integrated semigroup theory. As applications, the main theorem is used to obtain a known Hopf bifurcation resul...

Optimal control problems involving hybrid binary–continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity. Replacing such costs with their convex relaxation leads to a primal-dual optimality system that allows an explicit pointwise characterization and whose Moreau–Yosida regularization is amenable to a semismooth Newton method in function space. Thi...

This paper presents an algorithm for solving a class of large scale nonlinear programming problem which is originally derived from the multi-stage stochastic convex nonlinear programming. Using the Lagrangian-dual method and the Moreau-Yosida regularization, the primal problem is neatly transformed into a smooth convex problem. By introducing a self-concordant barrier function, an approximate g...

gives rise to a well-defined propagator, which is a semigroup of linear operators, and the theory of semigroups of linear operators on Banach spaces has developed quite rapidly since the discovery of the generation theorem byHille and Yosida in 1948. By now, it is a rich theory with substantial applications to many fields cf., e.g., 1–6 . In this paper, we pay attention to some basic problems o...