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Some non-smooth optimality results for optimization problems with vanishing constraints via Dini–Hadamard derivative

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Abstract

This research examines a wide class of optimization problems that are known in the literature as mathematical programs with vanishing constraints (MPVC for short). First, we introduce non-smooth stationarity conditions for MPVC and then we derive Fritz-John (FJ) and Karush–Khun–Tucker (KKT) type necessary conditions for isolated and local minima of a non-smooth MPVC in the framework of lower Dini–Hadamard derivative. Further, several sufficient conditions for such an MPVC are presented whereas the effective functions have pseudo-convex sublevel sets. The function class with pseudo-convex sublevel sets is a new class of extended convex functions that includes quasi-convex functions. In particular, we illustrate some of our results by examples.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, University of Qom, Qom, Iran

    Gholam Hasan Shirdel & Maryam Zeinali

  2. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, 88186-34141, Iran

    Ali Ansari Ardali

Authors
  1. Gholam Hasan Shirdel
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  2. Maryam Zeinali
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  3. Ali Ansari Ardali
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Correspondence to Gholam Hasan Shirdel.

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Shirdel, G.H., Zeinali, M. & Ansari Ardali, A. Some non-smooth optimality results for optimization problems with vanishing constraints via Dini–Hadamard derivative. J. Appl. Math. Comput. 68, 4099–4118 (2022). https://doi.org/10.1007/s12190-022-01698-y

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  • DOI: https://doi.org/10.1007/s12190-022-01698-y

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