Tien-Son Pham

activity

20152025

collaborators

5 papers

math.OC2025

Exact penalty functions in optimization with unbounded constraint sets

Liguo Jiao, Tien-Son Pham, Nguyen Van Tuyen

This paper identifies necessary and sufficient conditions for the exactness of penalty functions in optimization problems whose constraint sets are not necessarily bounded. The cas…

math.AG2024

Computation of the Łojasiewicz exponents of real bivariate analytic functions

Si Tiep Dinh, Feng Guo, Hong Duc Nguyen +1

The main goal of this paper is to present some explicit formulas for computing the {Ł}ojasiewicz exponent in the {Ł}ojasiewicz inequality comparing the rate of growth of two real b…

math.AP2021

The mountain pass theorem in terms of tangencies

Si Tiep Dinh, Tien Son Pham

This paper addresses the Mountain Pass Theorem for locally Lipschitz functions on finite-dimensional vector spaces in terms of tangencies. Namely, let $f \colon \mathbb R^n \to \ma…

math.OC2020

Stability of closedness of closed convex sets under linear mappings

Si Tiep Dinh, Tien Son Pham

We study the problem of when the continuous linear image of a fixed closed convex set $X \subset R^{n}$ is closed. Specifically, we improve the main results in the papers \ci…

math.AG2015

Łojasiewicz-type inequalities with explicit exponents for the largest eigenvalue function of real symmetric polynomial matrices

Si Tiep Dinh, Tien Son Pham

Let $F (x) := (f_{ij} (x))_{i, j = 1, \dots, p},$ be a real symmetric polynomial matrix of order $p$ and let $f (x)$ be the largest eigenvalue function of the matrix $F (x) .$ We denote by…