Coincidence Points of Parameterized Generalized Equations with Applications to Optimal Value Functions

Aram V. Arutyunov (), Boris S. Mordukhovich () and Sergey E. Zhukovskiy ()
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Aram V. Arutyunov: V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
Boris S. Mordukhovich: Wayne State University
Sergey E. Zhukovskiy: V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Journal of Optimization Theory and Applications, 2023, vol. 196, issue 1, No 8, 177-198

Abstract: Abstract 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 solutions of parameterized generalized equations, implicit function and fixed-point theorems, optimal value functions in parametric optimization, etc. Using the advanced machinery of variational analysis and generalized differentiation that furnishes complete characterizations of well-posedness properties of multifunctions, we establish a general theorem ensuring the existence of parameter-dependent coincidence point mappings with explicit error bounds for parameterized multifunctions between infinite-dimensional spaces. The obtained major result yields a new implicit function theorem and allows us to derive efficient conditions for semicontinuity and continuity of optimal value functions associated with parametric minimization problems subject to constraints governed by parameterized generalized equations.

Keywords: Variational analysis and generalized differentiation; Parametric optimization; Generalized equations; Coincidence and implicit function theorems; Optimal value functions; 49J52; 49J53; 47H10; 90C31 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-022-02140-w

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