On the existence of Pareto solutions for polynomial vector optimization problems
We are interested in the existence of Pareto solutions to the vector optimization problem Min
_ R^ m_+{f (x)\,|\, x ∈ R^ n\}, Min R+ mf (x)| x∈ R n, where f: R^ n → R^ mf: R n→ R m is a …
_ R^ m_+{f (x)\,|\, x ∈ R^ n\}, Min R+ mf (x)| x∈ R n, where f: R^ n → R^ mf: R n→ R m is a …
Existence of efficient and properly efficient solutions to problems of constrained vector optimization
DS Kim, BS Mordukhovich, TS Phạm… - Mathematical …, 2021 - Springer
The paper is devoted to the existence of global optimal solutions for a general class of
nonsmooth problems of constrained vector optimization without boundedness assumptions …
nonsmooth problems of constrained vector optimization without boundedness assumptions …
Atypical values and the Milnor set of real polynomials in two variables
GE Monsalve - Bulletin of the Brazilian Mathematical Society, New …, 2023 - Springer
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Polar degree and vanishing cycles
We prove that the polar degree of an arbitrarily singular projective hypersurface can be
decomposed as a sum of non‐negative numbers which quantify local vanishing cycles of …
decomposed as a sum of non‐negative numbers which quantify local vanishing cycles of …
Atypical points at infinity and algorithmic detection of the bifurcation locus of real polynomials
We show that the variation of the topology at infinity of a two-variable polynomial function is
localisable at a finite number of “atypical points” at infinity. We construct an effective …
localisable at a finite number of “atypical points” at infinity. We construct an effective …
Global index of real polynomials
GE Monsalve, M Tibăr - Proceedings of the Royal Society of …, 2024 - cambridge.org
Global index of real polynomials Page 1 Proceedings of the Royal Society of Edinburgh,
page 1 of 29 DOI:10.1017/prm.2024.23 Global index of real polynomials Gabriel E. Monsalve …
page 1 of 29 DOI:10.1017/prm.2024.23 Global index of real polynomials Gabriel E. Monsalve …
The tropical discriminant of a polynomial map on a plane
BE Hilany - arXiv preprint arXiv:2202.05052, 2022 - arxiv.org
The discriminant of a polynomial map is central to problems from affine geometry and
singularity theory. Standard methods for characterizing it rely on elimination techniques that …
singularity theory. Standard methods for characterizing it rely on elimination techniques that …
[PDF][PDF] On real curve construction for asymptotic critical value set of a polynomial map
ON REAL CURVE CONSTRUCTION FOR ASYMPTOTIC CRITICAL VALUE SET OF A
POLYNOMIAL MAP Page 1 Доклади на Българската академия на науките Comptes …
POLYNOMIAL MAP Page 1 Доклади на Българската академия на науките Comptes …
Existence of Pareto Solutions for Vector Polynomial Optimization Problems with Constraints
Y Duan, L Jiao, P Wu, Y Zhou - Journal of Optimization Theory and …, 2022 - Springer
This paper deals with a vector polynomial optimization problem over a basic closed semi-
algebraic set. By invoking some powerful tools from real semi-algebraic geometry, we first …
algebraic set. By invoking some powerful tools from real semi-algebraic geometry, we first …
[PDF][PDF] Computing efficiently the non-properness set of polynomial maps on the plane
B El Hilany, E Tsigaridas - arXiv preprint arXiv, 2021 - puremath.no
We introduce novel mathematical and computational tools to develop a complete and
efficient algorithm for computing the set of non-properness of polynomial maps on the plane …
efficient algorithm for computing the set of non-properness of polynomial maps on the plane …