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Logarithmic Expansion, Entropy, and Dimension for Set-Valued Maps
We obtain a lower bound for the entropy of a Borel probability measure (not necessarily invariant) with respect to an upper semicontinuous set-valued...
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Second-order optimality conditions for set-valued optimization problems under the set criterion
This paper investigates second-order optimality conditions for general constrained set-valued optimization problems in normed vector spaces under the...
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Topological Stability and Entropy for Certain Set-valued Maps
In this paper, the dynamics (including shadowing property, expansiveness, topological stability and entropy) of several types of upper...
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Topological Entropy of Iterated Set-Valued Dynamical Systems
This paper studies topological entropy and pseudo-entropy of iterated set-valued function systems. Firstly, the notions of topological entropy...
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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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Set-Valued Model Predictive Control
This chapter presents a formulation for model predictive control (MPC) where system dynamics are represented in terms of sets. This formulation can...
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Characteristic curves for Set-Valued Hamilton-Jacobi Equations
The method of characteristics is extended to set-valued Hamilton-Jacobi equations. This problem arises from a calculus of variations’ problem with a...
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A Notion of Fenchel Conjugate for Set-Valued Map**s
In this paper, we present a novel concept of the Fenchel conjugate for set-valued map**s and investigate its properties in finite and infinite...
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Metric Regularity for Set-Valued Maps in Fréchet-Montel Spaces. Implicit Map** Theorem
This paper is devoted to new derivative criterion of metric regularity for set-valued map from a Fréchet-Montel space to a Fréchet space. Such type...
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Approximate Benson properly efficient solutions for set-valued equilibrium problems
In this paper, we introduce the concept of approximate Benson properly efficient solutions for the set-valued equilibrium problems (in short, SVEP)...
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Tree-likeness of inverse limits with set-valued bonding functions
In this paper, we establish conditions under which the inverse limits with set-valued bonding functions are tree-like continua. We show that if we...
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Treatment of Set-Valued Robustness via Separation and Scalarization
This paper aims to present alternative characterizations for different types of set-valued robustness concepts. Equivalent scalar representations for...
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Higher-order generalized tangent epiderivatives and applications to set-valued optimization
In the paper, we introduce two new concepts on differentiability for set-valued maps, named by the higher-order generalized tangent epiderivative and...
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Set-valued Data
Since fuzzy sets are generalizations of ordinary sets, we present in this Chapter the essentials of random set theory for statistics. This material...
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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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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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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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Quasi-Error Bounds for p-Convex Set-Valued Map**s
We first introduce the concept of p -convex set-valued map**s, which is an extension of p -convex functions. Then, we show that for a p -convex set...
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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...