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Random Lift of Set Valued Maps and Applications to Multiagent Dynamics
We introduce an abstract framework for the study of general mean field games and mean field control problems. Given a multiagent system, its...
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Generalized Lagrangian Duality in Set-valued Vector Optimization via Abstract Subdifferential
In this paper, we investigate dual problems for nonconvex set-valued vector optimization via abstract subdifferential. We first introduce a...
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Probability Functions Generated by Set-Valued Map**s: A Study of First Order Information
Probability functions appear in constraints of many optimization problems in practice and have become quite popular. Understanding their first-order...
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Pareto epsilon-subdifferential sum rule for set-valued map**s and applications to set optimization
In this paper, we are mainly concerned with a rule for efficient (Pareto) approximate subdifferential, concerning the sum of two cone-convex...
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Directional derivatives and subdifferentials for set-valued maps applied to set optimization
We present a general method to devise directional derivatives and subdifferentials for set-valued maps that generalize the corresponding...
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Optimality conditions for robust weakly efficient solutions in uncertain optimization
In this paper, we find the flimsily robust weakly efficient solution to the uncertain vector optimization problem by means of the weighted sum...
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On the Eventual Shadowing Property and Eventually Shadowable Point of Set-valued Dynamical Systems
The authors introduce the concepts of the eventual shadowing property and eventually shadowable point for set-valued dynamical systems and prove that...
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Stability in Set-Valued Optimization Problems Using Asymptotic Analysis and Epi-Convergence
We study the stability of set-valued optimization problems by using epi-convergence coupled with asymptotic analysis. To do this, we recall the...
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Approximate Weak Minimal Solutions of Set-Valued Optimization Problems
This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria. The...
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Using ρ-cone arcwise connectedness on parametric set-valued optimization problems
Within the inquiry about work, we explore a parametric set-valued optimization problem, where the objective as well as constraint maps are...
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Higher-order set-valued Hadamard directional derivatives: calculus rules and sensitivity analysis of equilibrium problems and generalized equations
In this paper, we propose a notion of higher-order directional derivatives in the sense of Hadamard for set-valued maps, which is a natural extension...
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Dynamics with Set-Valued Functions and Coselections
We study dynamical systems with upper semicontinuous functions and coselections. We define the appropriate versions of dynamic properties on...
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Karush–Kuhn–Tucker Multiplier Rules for Efficient Solutions of Set-Valued Equilibrium Problem with Constraints
In this paper, a type of contingent derivative of a set-valued map is proposed and applied to investigate some necessary optimality conditions for...
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Set-valued parametric optimization problems with higher-order \(\rho \)-cone arcwise connectedness
In this study, we take into account the set-valued parametric optimization problem ( PP ) (abbreviated as SVPOP), in which both the objective and...
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Probabilistic Characterization of Weakly Harmonic Maps with Respect to Non-Local Dirichlet Forms
We characterize weakly harmonic maps with respect to non-local Dirichlet forms by Markov processes and martingales. In particular, we can obtain...
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A Steepest Descent Method for Set Optimization Problems with Set-Valued Map**s of Finite Cardinality
In this paper, we study a first-order solution method for a particular class of set optimization problems where the solution concept is given by the...
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Regularity and Compactness of Stationary Map-Varifold Pairs
The authors introduce the conception of stationary map-varifold pairs and prove a compactness result. As applications, they analyse the asymptotic...
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Lower Characteristic, Weakly Quasi-compact and Application
In this paper, we present some results concerning the weakly quasi-compact and lower characteristic operators. An application to Markov chains, is...
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On the Shadowing Property and Shadowable Point of Set-valued Dynamical Systems
In this article, the authors introduce the concept of shadowable points for set-valued dynamical systems, the pointwise version of the shadowing...