Weak sharp minima at infinity and solution stability in mathematical programming via asymptotic analysis

Felipe Lara; Nguyen Van Tuyen; Tran Van Nghi

doi:10.1007/s10898-025-01516-2

Weak sharp minima at infinity and solution stability in mathematical programming via asymptotic analysis

Felipe Lara
, Nguyen Van Tuyen
, Tran Van Nghi

Institute of Higher Research

Hanoi Pedagogical University 2

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also useful for studying the solution stability of nonconvex optimization problems under linear perturbations. Finally, we provide applications for a subclass of quasiconvex functions which is stable under linear additivity and includes the convex ones.

Original language	English
Pages (from-to)	933-950
Number of pages	18
Journal	Journal of Global Optimization
Volume	92
Issue number	4
DOIs	https://doi.org/10.1007/s10898-025-01516-2
State	Published - Aug 2025

Keywords

49J52
49J53
49K30
49K40
90C26
90C31
Asymptotic cone
Asymptotic function
Linear perturbation
Solution stability
Weak sharp minima at infinity

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10.1007/s10898-025-01516-2

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title = "Weak sharp minima at infinity and solution stability in mathematical programming via asymptotic analysis",

abstract = "We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also useful for studying the solution stability of nonconvex optimization problems under linear perturbations. Finally, we provide applications for a subclass of quasiconvex functions which is stable under linear additivity and includes the convex ones.",

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author = "Felipe Lara and \{Van Tuyen\}, Nguyen and \{Van Nghi\}, Tran",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.",

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doi = "10.1007/s10898-025-01516-2",

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T1 - Weak sharp minima at infinity and solution stability in mathematical programming via asymptotic analysis

AU - Lara, Felipe

AU - Van Tuyen, Nguyen

AU - Van Nghi, Tran

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025/8

Y1 - 2025/8

N2 - We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also useful for studying the solution stability of nonconvex optimization problems under linear perturbations. Finally, we provide applications for a subclass of quasiconvex functions which is stable under linear additivity and includes the convex ones.

AB - We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also useful for studying the solution stability of nonconvex optimization problems under linear perturbations. Finally, we provide applications for a subclass of quasiconvex functions which is stable under linear additivity and includes the convex ones.

KW - 49J52

KW - 49J53

KW - 49K30

KW - 49K40

KW - 90C26

KW - 90C31

KW - Asymptotic cone

KW - Asymptotic function

KW - Linear perturbation

KW - Solution stability

KW - Weak sharp minima at infinity

UR - https://www.scopus.com/pages/publications/105008966506

U2 - 10.1007/s10898-025-01516-2

DO - 10.1007/s10898-025-01516-2

M3 - Article

AN - SCOPUS:105008966506

SN - 0925-5001

VL - 92

SP - 933

EP - 950

JO - Journal of Global Optimization

JF - Journal of Global Optimization

IS - 4

ER -

Weak sharp minima at infinity and solution stability in mathematical programming via asymptotic analysis

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Keywords

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