On implicit function theorem for locally Lipschitz equations

Arutyunov, A. V.; Zhukovskiy, S. E.

doi:10.1007/s10107-021-01750-y

Cited by 3 publications

(2 citation statements)

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“…On the other hand, the emphasis of the analysis is here on global properties of S, instead of the local ones. Nonlocal implicit function theorems for traditional equation systems, under a topological space parametrization, have been recently addressed also in [4], which inspired the present research work.…”

Section: Introductionmentioning

confidence: 93%

“…Following a recent approach to the theory of implicit and inverse functions and to the theory of fixed and coincidence points (see [2][3][4]), the existence of problem solutions will be achieved by minimizing proper functions, which are shown to satisfy a Caristi-type condition. Recall that a function ϕ : X −→ [0, +∞] is said to satisfy a Caristi-type condition if there exists a constant κ > 0 such that…”

Section: Preliminariesmentioning

confidence: 99%

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Conditions for the stability of ideal efficient solutions in parametric vector optimization via set-valued inclusions

Uderzo

2022

J Glob Optim

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In present paper, an analysis of the stability behaviour of ideal efficient solutions to parametric vector optimization problems is conducted. A sufficient condition for the existence of ideal efficient solutions to locally perturbed problems and their nearness to a given reference value is provided by refining recent results on the stability theory of parameterized set-valued inclusions. More precisely, the Lipschitz lower semicontinuity property of the solution mapping is established, with an estimate of the related modulus. A notable consequence of this fact is the calmness behaviour of the ideal value mapping associated to the parametric class of vector optimization problems. Within such an analysis, a refinement of a recent existence result, specific for ideal efficient solutions to unperturbed problem and enhanced by related error bounds, is discussed. Some connections with the concept of robustness in multi-objective optimization are also sketched.

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Section: Introductionmentioning

confidence: 93%

Section: Preliminariesmentioning

confidence: 99%