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Second-Order Variational Analysis in Optimization, Variational Stability, and Control Theory, Algorithms, Applications
This fundamental work is a sequel to monographs by the same author: Variational Analysis and Applications (2018) and the two Grundlehren volumes Variat...
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Variational Principles
The term ‘variational principle’, which was formerly attached to laws of nature asserting that some quantity is minimized, is now used to describe...
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Variational and Quasi-Variational Inequalities Under Local Reproducibility: Solution Concept and Applications
Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in...
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Generalized Nash Equilibrium from a Robustness Perspective in Variational Analysis
Generalized Nash equilibrium is updated by a formulation in terms of extended-real-valued functions being minimized by the agents. Tools of...
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Variational Analysis
Abstract Text
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Role of Subgradients in Variational Analysis of Polyhedral Functions
Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of...
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Optimal Analysis of Method with Batching for Monotone Stochastic Finite-Sum Variational Inequalities
AbstractVariational inequalities are a universal optimization paradigm that is interesting in itself, but also incorporates classical minimization...
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Variational Analysis
In this chapter, we present some subjects related to variational analysis. In Sect. 8.1, we introduce some modes of set convergence, examine the...
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Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models
Multilevel Stein variational gradient descent is a method for particle-based variational inference that leverages hierarchies of surrogate target...
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Sensitivity Analysis of Stochastic Constraint and Variational Systems via Generalized Differentiation
This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational...
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Variational Analysis of Norm Cones in Finite Dimensional Euclidean Spaces
A norm cone in a finite dimensional Euclidean space is the epigraph of a norm. Many important practical optimization problems are formulated as norm...
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Stability analysis for set-valued inverse mixed variational inequalities in reflexive Banach spaces
This work is devoted to the analysis for a new class of set-valued inverse mixed variational inequalities (SIMVIs) in reflexive Banach spaces, when...
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Variational Analysis Based on Proximal Subdifferential on Smooth Banach Spaces
This paper first shows that for any p ∈ (1, 2) there exists a continuously differentiable function f on l p (and L p ) such that the proximal...
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Variational Principles in Quaternionic Analysis with Applications to the Stationary MHD Equations
In this paper we aim to combine tools from variational calculus with modern techniques from quaternionic analysis that involve Dirac type operators...
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Young Duality of Variational Inequalities. An Application for the Analysis of Interactions in Production Networks
We develop a mathematical technique of Young dual variational inequalities, which are used to model market equilibrium in a network of production...
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Scalar, Multidimensional Variational Problems
Once we have established a solid functional-analytical foundation, we are ready to tackle multidimensional variational problems in which we pretend...
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Variational Inequalities
In this chapter we present well-posedness results for variational inequalities.
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Lectures on Variational Analysis
This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations,...
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First- and second-order optimality conditions of nonsmooth sparsity multiobjective optimization via variational analysis
In this paper, we investigate optimality conditions of nonsmooth sparsity multiobjective optimization problem (shortly, SMOP) by the advanced...
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Analysis and Numerical Approximation of Energy-Variational Solutions to the Ericksen–Leslie Equations
We define the concept of energy-variational solutions for the Ericksen–Leslie equations in three spatial dimensions. This solution concept is finer...
