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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Aram V. Arutyunov & Boris S. Mordukhovich & Sergey E. Zhukovskiy, 2023. "Coincidence Points of Parameterized Generalized Equations with Applications to Optimal Value Functions," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 177-198, January.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:1:d:10.1007_s10957-022-02140-w
    DOI: 10.1007/s10957-022-02140-w
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    References listed on IDEAS

    as
    1. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    2. T. Q. Bao & P. Gupta & B. S. Mordukhovich, 2007. "Necessary Conditions in Multiobjective Optimization with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 179-203, November.
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