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Hadamard well posedness for set optimization

Hadamard transform

Nonlinear system

Constraint (computer-aided design)

Convergence (economics)

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Hadamard well-posedness in set optimization is extensively studied in various research papers. Tran Quoc Duy et al. establish Hadamard well-posedness properties for efficient and weakly efficient solutions in a set optimization problem with an infinite number of constraints, utilizing Kuroiwa's lower set less relation and weak Slater constraint qualification . Geoffroy and Larrouy introduce a topology on the power set of a normed space to address set optimization problems, deriving concepts of continuity and semicontinuity for set-valued mappings . Miholca extends the concept of well-posedness to set-valued equilibrium problems in topological vector spaces, providing sufficient conditions and introducing minimizing sequences for relaxation . Zhang et al. explore well-posedness and stability in set optimization, characterizing different types of well-posedness and studying minimal solution mappings for parametric set optimization . Additionally, a study by Zhang et al. considers Gerstewitz scalarization function to investigate minimal solutions and well-posedness in set optimization problems .

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Book Chapter•DOI Well-Posedness of Set Optimization Using Nonlinear Scalarization Function 15 Jul 2022	The paper addresses well-posedness of set optimization using Gerstewitz scalarization function, establishing conditions for well-posedness and equivalence between set and scalar optimization problems.
Journal Article•DOI Well-posedness and stability in set optimization with applications Chuang-liang Zhang, Chuang-liang Zhang, Nan-jing Huang - Show less +2 more 19 Jan 2021-Positivity 8 Citations	The paper discusses well-posedness in set optimization, including Hadamard well-posedness, with characterizations and conditions under mild assumptions, utilizing local C-Lipschitz continuity for analysis.
Journal Article•DOI A New Topological Framework and Its Application to Well-Posedness in Set-Valued Optimization Michel H. Geoffroy, James Larrouy - Show less +1 more 08 Nov 2022-Numerical Functional Analysis and Optimization	The paper introduces a new topological framework for set-valued optimization, addressing well-posedness through a cone ordering, providing a basis for Hadamard well-posedness in set optimization.
Open access•Journal Article•DOI Well-posedness for set-valued equilibrium problems Mihaela Miholca 10 Mar 2022-Studia Universitatis Babeş-Bolyai	The paper discusses well-posedness for set-valued equilibrium problems, extending the concept to set optimization with sufficient conditions provided in generalized convex settings.
Journal Article•DOI Hadamard well-posedness for a set optimization problem with an infinite number of constraints Tran Quoc Duy 24 Jan 2023-Optimization 1 Citations	The paper discusses Hadamard well-posedness for a set optimization problem with an infinite number of constraints, establishing conditions for efficient solutions under functional perturbations.

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