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Error bounds: Necessary and sufficient conditions
, 2010
"... The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivativelike objects both from the primal as well as from the dual space ..."
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Cited by 17 (6 self)
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The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivativelike objects both from the primal as well as from the dual space
About regularity of set systems
 University of Ballarat
"... Abstract. Extremality, stationarity and regularity notions for a system of closed sets in a normed linear space are investigated. The equivalence of different abstract “extremal” settings in terms of set systems and multifunctions is proved. The dual necessary and sufficient conditions of weak stati ..."
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Cited by 8 (3 self)
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Abstract. Extremality, stationarity and regularity notions for a system of closed sets in a normed linear space are investigated. The equivalence of different abstract “extremal” settings in terms of set systems and multifunctions is proved. The dual necessary and sufficient conditions of weak stationarity (the Extended extremal principle) are presented for the case of an Asplund space. 1.
EKELAND’S VARIATIONAL PRINCIPLE FOR SETVALUED FUNCTIONS
"... Abstract. We establish several setvalued function versions of Ekeland’s variational principle and hence provide some sufficient conditions ensuring the existence of error bounds for inequality systems defined by finitely many lower semicontinuous functions. ..."
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Cited by 4 (0 self)
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Abstract. We establish several setvalued function versions of Ekeland’s variational principle and hence provide some sufficient conditions ensuring the existence of error bounds for inequality systems defined by finitely many lower semicontinuous functions.
Stationarity and Regularity of Infinite Collections of Sets. Applications to Infinitely Constrained Optimization
 J OPTIM THEORY APPL
, 2011
"... This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger and López: J Optim. Theory Appl. 154(2) (2012), and is mainly focused on the application of the stationarity criteria to infinitely constrained optim ..."
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Cited by 3 (1 self)
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This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger and López: J Optim. Theory Appl. 154(2) (2012), and is mainly focused on the application of the stationarity criteria to infinitely constrained optimization problems. We consider several settings of optimization problems, which involve (explicitly or implicitly) infinite collections of sets and deduce for them necessary conditions characterizing stationarity in terms of dual space elements – normals and/or subdifferentials.
ERROR BOUNDS FOR VECTORVALUED FUNCTIONS: NECESSARY AND SUFFICIENT CONDITIONS
, 2011
"... In this paper, we attempt to extend the definition and existing local error bound criteria to vectorvalued functions, or more generally, to functions taking values in a normed linear space. Some new derivativelike objects (slopes and subdifferentials) are introduced and a general classification sc ..."
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Cited by 2 (1 self)
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In this paper, we attempt to extend the definition and existing local error bound criteria to vectorvalued functions, or more generally, to functions taking values in a normed linear space. Some new derivativelike objects (slopes and subdifferentials) are introduced and a general classification scheme of error bound criteria is presented.
National Natural Science Foundation of China (11101248, 71101140), Shandong Province Natural Science Foundation (ZR2010AQ026), and Young Teacher
, 2012
"... Abstract. In this paper, we deal with the semiinfinite complementarity problems (SICP), in which several important issues are covered, such as solvability, semismoothness of residual functions, and error bounds. In particular, we characterize the solution set by investigating the relationship betw ..."
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Abstract. In this paper, we deal with the semiinfinite complementarity problems (SICP), in which several important issues are covered, such as solvability, semismoothness of residual functions, and error bounds. In particular, we characterize the solution set by investigating the relationship between SICP and the classical complementarity problem. 1 Furthermore, we show that the SICP can be equivalently reformulated as a typical semiinfinite minmax programming problem by employing NCP functions. Finally, we study the concept of error bounds and introduce its two variants, εerror bounds and weak error bounds, where the concept of weak error bounds is highly desirable in that the solution set is not restricted to be nonempty. Key words. semiinfinite complementarity problem, semidifferentiable and semismooth, error bounds, weak error bounds.
Global Error
"... bounds for systems of convex polynomials over polyhedral constraints ..."
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Stability of error bounds for convex constraint systems in Banach spaces
, 2010
"... This paper studies stability of error bounds for convex constraint systems in Banach spaces. We show that certain known sufficient conditions for local and global error bounds actually ensure error bounds for the family of functions being in a sense small perturbations of the given one. A single ine ..."
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This paper studies stability of error bounds for convex constraint systems in Banach spaces. We show that certain known sufficient conditions for local and global error bounds actually ensure error bounds for the family of functions being in a sense small perturbations of the given one. A single inequality as well as semiinfinite constraint systems are considered.
ERROR BOUNDS FOR VECTORVALUED FUNCTIONS ON METRIC SPACES
, 2011
"... In this paper, we attempt to extend the definition and existing local error bound criteria to vectorvalued functions, or more generally, to functions taking values in a normed linear space. Some new primal space derivativelike objects – slopes – are introduced and a classification scheme of erro ..."
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In this paper, we attempt to extend the definition and existing local error bound criteria to vectorvalued functions, or more generally, to functions taking values in a normed linear space. Some new primal space derivativelike objects – slopes – are introduced and a classification scheme of error bound criteria is presented.