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Nonlinear scalarization in set optimization based on the concept of null set
The aim of this paper is to introduce a nonlinear scalarization function in set optimization based on the concept of null set which was introduced by...
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Cone-Compactness of a Set and Applications to Set-Equilibrium Problems
We study the possibility to get a sequential characterization of the compactness of a set with respect to a cone. Then, we consider some...
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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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Point-Set Topology A Working Textbook
This textbook offers a hands-on introduction to general topology, a fundamental tool in mathematics and its applications. It provides solid...
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On scalarization and well-posedness in set optimization with a partial set order relation
In this paper, a new scalarization function is introduced with respect to a partial set order relation established by Karaman et al. (Positivity...
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Optimization of the Reachable Set of a Linear System with Respect to Another Set
AbstractGiven a linear controlled autonomous system, we consider the problem of including a convex compact set in the reachable set of the system in...
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Safe Set Theory
This chapter introduces Russell’s idea that sets are built by stages. This avoids the obvious contradictions of the naïve set theory of Cantor’s that...
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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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The Set of Limiting Realizable Values of Topological Entropy of Continuous Map**s of a Cantor Set
AbstractIt is established that in any neighborhood of each continuous map** of a Cantor perfect set there is a map** with a given topological...
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Set Theory
In this chapter, I present the foundational results of set theory. I introduce all the axioms for the set theory and then build up the necessary...
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Directional Derivative and Subgradient of Cone-Convex Set-Valued Map**s with Applications in Set Optimization Problems
In this paper, we introduce a new directional derivative and subgradient of set-valued map**s by using a nonlinear scalarizing function. We obtain...
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Besov wavefront set
We develop a notion of wavefront set aimed at characterizing in Fourier space the directions along which a distribution behaves or not as an element...
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The Aubry Set and Mather Set in the Embedded Contact Hamiltonian System
We embed the Aubry set and Mather set in the Tonelli Hamiltonian system to the contact Hamiltonian system. We find the embedded Aubry set is the set...
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New Notions of Proper Efficiency in Set Optimization with the Set Criterion
In this paper, we introduce new notions of proper efficiency in the sense of Henig for a set optimization problem by using the set criterion of...
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Sensitivity Analysis of the Set of Sustainable Thresholds
In the context of constrained control-systems, the Set of Sustainable Thresholds plays in a sense the role of a dual object to the so-called...
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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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Mathematical analysis of modified level-set equations
The linear transport equation allows to advect level-set functions to represent moving sharp interfaces in multiphase flows as zero level-sets. A...
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Mosco convergence of set-valued supermartingale
The existence of regular martingale selectors for multivalued supermartingales with unbounded values in a separable Banach space Y is proved. In...
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Set-Driven Evolution for Multiagent System
We consider the deterministic evolution in the Euclidean space of a multiagent system with a large number of agents (possibly infinitely many). At...