Related papers: An implicit multifunction theorem for the hemiregu…
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…
In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is…
In this article we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be…
The present paper deals with the perturbation analysis of set-valued inclusion problems, a problem format whose relevance has recently emerged in such contexts as robust and vector optimization as well as in vector equilibrium theory. The…
In this paper, we introduce a new method for applying the implicit function theorem to find nontrivial solutions to overdetermined problems with a fixed boundary (given) and a free boundary (to be determined). The novelty of this method…
In this paper we aim to present two general results regarding, on one hand, the openness stability of set-valued maps and, on the other hand, the metric regularity behavior of the implicit multifunction related to a generalized variational…
The subject of the present paper are stability properties of the solution set to set-valued inclusions. The latter are problems emerging in robust optimization and mathematical economics, which can not be cast in traditional generalized…
We propose an implicit iterative algorithm for an exact penalty method arising from inequality constrained optimization problems. A rapidly convergent fixed point method is developed for a regularized penalty functional. The applicability…
Mathematically characterizing the implicit regularization induced by gradient-based optimization is a longstanding pursuit in the theory of deep learning. A widespread hope is that a characterization based on minimization of norms may…
In present paper, an analysis of the stability behaviour of ideal efficient solutions to parametric vector optimization problems is conducted. A sufficient condition for the existence of ideal efficient solutions to locally perturbed…
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
In this paper, we introduce a new class of optimization problems whose objective functions are weakly homogeneous relative to the constraint sets. By using the normalization argument in asymptotic analysis, we prove two criteria for the…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…
The paper is devoted to the development of new sufficient conditions for the calmness and the Aubin property of implicit multifunctions. As the basic tool one employs the directional limiting coderivative which, together with the graphical…
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…
We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical…
In this paper, we propose a general class of algorithms for optimizing an extensive variety of nonsmoothly penalized objective functions that satisfy certain regularity conditions. The proposed framework utilizes the…
This work studies the multi-task functional linear regression models where both the covariates and the unknown regression coefficients (called slope functions) are curves. For slope function estimation, we employ penalized splines to…