Related papers: On Subregularity Properties of Set-Valued Mappings…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
Submodular optimization has received significant attention in both practice and theory, as a wide array of problems in machine learning, auction theory, and combinatorial optimization have submodular structure. In practice, these problems…
The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in…
This is a review paper, summarizing without proofs recent results by the authors on the property of strong metric subregularity (SMSR) in optimization. It presents sufficient conditions for SMSR of the optimality mapping associated with a…
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
Biased regularization and fine-tuning are two recent meta-learning approaches. They have been shown to be effective to tackle distributions of tasks, in which the tasks' target vectors are all close to a common meta-parameter vector.…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from…
In this article, we develop a trust-region technique to find critical points of unconstrained set optimization problems with the objective set-valued map defined by finitely many twice continuously differentiable functions. The technique is…
In this work, we study the external and internal stability of minimal solutions to set-valued optimization problems in a new functional framework. We consider perturbations on both the objective function and the admissible domain. To…
Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems.…
In the present paper, several properties concerning generalized derivatives of multifunctions implicitly defined by set-valued inclusions are studied by techniques of variational analysis. Set-valued inclusions are problems formalizing the…
In many learning tasks, the structure of the target space of a function holds rich information about the relationships between evaluations of functions on different data points. Existing approaches attempt to exploit this relationship…
This is mainly a survey on the properties of Strong Metric Regularity (SMR) and Strong Metric subRegularity (SMsR) of mappings representing first order optimality conditions (so-called optimality mappings) of optimization problems in…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
This paper is devoted to studying of some properties of multivalued mappings in Euclidean space. There were proved theorems on a fixed point for multivalued mappings whose restrictions to some subset in the closure of a domain satisfy "a…
We provide necessary and sufficient conditions for a set-valued mapping between finite dimensional spaces to be directionally open by relating this property with directional regularity, H\"older continuity of the inverse mapping,…