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Related papers: Coderivatives at infinity of set-valued mappings

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This paper concerns generalized differential characterizations of maximal monotone set-valued mappings. Using advanced tools of variational analysis, we establish coderivative criteria for maximal monotonicity of set-valued mappings, which…

Optimization and Control · Mathematics 2015-01-05 N. H. Chieu , G. M. Lee , B. S. Mordukhovich , T. T. A. Nghia

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…

Functional Analysis · Mathematics 2012-10-16 Marius Durea , Van Ngai Huynh , Huu Tron Nguyen , Radu Strugariu

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,…

Optimization and Control · Mathematics 2022-07-26 Si Tiep Dinh , Tien Son Pham

In this paper, we present a novel concept of the Fenchel conjugate for set-valued mappings and investigate its properties in finite and infinite dimensions. After establishing the fundamental properties of the Fenchel conjugate for…

Optimization and Control · Mathematics 2023-11-07 Nguyen Mau Nam , Gary Sandine , Nguyen Nang Thieu , Nguyen Dong Yen

In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…

Optimization and Control · Mathematics 2012-02-07 Marius Apetrii , Marius Durea , Radu Strugariu

The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…

Optimization and Control · Mathematics 2024-10-16 Boris S. Mordukhovich , Oanh Nguyen

The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…

Optimization and Control · Mathematics 2022-03-23 Aram V. Arutyunov , Boris S. Mordukhovich , Sergey E. Zhukovskiy

In this paper we will establish some necessary condition and sufficient condition respectively for a set-valued mapping to have the Lipschitz-like property relative to a closed set by employing regular normal cone and limiting normal cone…

Optimization and Control · Mathematics 2020-09-23 Kaiwen Meng , Minghua Li , Wenfang Yao , Xiaoqi Yang

In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the…

Optimization and Control · Mathematics 2011-02-28 Boris S. Mordukhovich , Hung M. Phan

For a set-valued map, we characterize, in terms of its (unconvexified or convexified) graphical derivatives near the point of interest, positively homogeneous maps that are generalized derivatives in the sense of [20]. This result…

Optimization and Control · Mathematics 2012-11-20 C. H. Jeffrey Pang

Among other results, the paper gives new mapping theorems and new fixed point property theorems for inverse limits of inverse sequences of compact metric spaces with upper semicontinuous set-valued bonding functions. We also revisit the…

Dynamical Systems · Mathematics 2021-12-14 Iztok Banic , Goran Erceg , Judy Kennedy

We consider vector and set optimization problems with respect to variable domination structures given by set-valued mappings acting between the preimage space and the image space of the objective mapping, as well as by set-valued mappings…

Optimization and Control · Mathematics 2025-03-11 Marius Durea , Christian Günther , Radu Strugariu , Christiane Tammer

The aim of this paper is to establish some results regarding Infinite Iterated Function Systems with the help of the Tarski-Kantorovitch fixed-point principles for maps on partially ordered sets. To this end we introduce two new classes of…

Dynamical Systems · Mathematics 2021-10-12 Bogdan-Alexandru Luchian

This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…

Optimization and Control · Mathematics 2025-10-13 Le Ngoc Kien , Nguyen Van Tuyen , Tran Van Nghi

In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions objects are…

Optimization and Control · Mathematics 2023-08-01 Do Sang Kim , Minh Tung Nguyen , Tien Son Pham

In this paper, we propose criteria for unboundedness of the images of set-valued mappings having closed graphs in Euclidean spaces. We focus on mappings whose domains are non-closed or whose values are connected. These criteria allow us to…

Optimization and Control · Mathematics 2024-09-24 Vu Trung Hieu , Elisabeth Anna Sophia Köbis , Markus Arthur Köbis , Paul Hugo Schmölling

In Part 1 of this paper, we have estimated the Fr\'echet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem with one smooth functional constraint under total…

Optimization and Control · Mathematics 2018-11-15 Duong Thi Kim Huyen , Jen-Chih Yao , Nguyen Dong Yen

In this paper we consider dynamical properties of set-valued mappings and their implications on the associated inverse limit space. Specifically, we define the specification property and topological entropy for set-valued functions and…

Dynamical Systems · Mathematics 2015-09-29 Brian Raines , Tim Tennant

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…

Optimization and Control · Mathematics 2020-06-23 Amos Uderzo

By applying some theorems of Levy and Mordukhovich (Math Program 99: 311--327, 2004) and other related results, we estimate the Fr\'echet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric…

Optimization and Control · Mathematics 2018-11-15 Duong Thi Kim Huyen , Jen-Chih Yao , Nguyen Dong Yen
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