54 citations · 92 across the 14 of their papers we have counts for
14 papers
Piecewise SOS-Convex Moment Optimization and Applications via Exact Semi-Definite Programs
Queenie Yingkun Huang, Vaithilingam Jeyakumar, Guoyin Li
This paper presents exact Semi-Definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-c…
Calculating Radius of Robust Feasibility of Uncertain Linear Conic Programs via Semidefinite Programs
Miguel A. Goberna, Vaithilingam Jeyakumar, Guoyin Li
The radius of robust feasibility provides a numerical value for the largest possible uncertainty set that guarantees robust feasibility of an uncertain linear conic program. This d…
Exact Conic Programming Reformulations of Two-Stage Adjustable Robust Linear Programs with New Quadratic Decision Rules
D. Woolnough, V. Jeyakumar, G. Li
In this paper we introduce a new parameterized Quadratic Decision Rule (QDR), a generalisation of the commonly employed Affine Decision Rule (ADR), for two-stage linear adjustable…
A Bounded Degree Lasserre Hierarchy with SOCP Relaxations for Global Polynomial Optimization and Applications
T. D Chuong, V. Jeyakumar, G. Li
In this paper, we propose a new convergent conic programming hierarchy of relaxations involving both semi-definite cone and second-order cone constraints for solving nonconvex poly…
Convexifiability of Continuous and Discrete Nonnegative Quadratic Programs for Gap-Free Duality
N. H. Chieu, V. Jeyakumar, G. Li
In this paper we show that a convexifiability property of nonconvex quadratic programs with nonnegative variables and quadratic constraints guarantees zero duality gap between the…
Extended Trust-Region Problems with One or Two Balls: Exact Copositive and Lagrangian Relaxations
I. M. Bomze, V. Jeyakumar, G. Li
We establish a geometric condition guaranteeing exact copositive relaxation for the nonconvex quadratic optimization problem under two quadratic and several linear constraints, and…
Robust Global Solutions of Bilevel Polynomial Optimization Problems with Uncertain Linear Constraints
T. D. Chuong, V. Jeyakumar
This paper studies, for the first time, a bilevel polynomial program whose constraints involve uncertain linear constraints and another uncertain linear optimization problem. In th…
Convergent Semidefinite Programming Relaxations for Global Bilevel Polynomial Optimization Problems
V. Jeyakumar, J. B. Lasserre, G. Li +1
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials…
Robust Solutions to Multi-Objective Linear Programs with Uncertain Data
M. A. Goberna, V. Jeyakumar, G. Li +1
In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula…
Trust--Region Problems with Linear Inequality Constraints: Exact SDP Relaxation, Global Optimality and Robust Optimization
V. Jeyakumar, G. Li
The trust-region problem, which minimizes a nonconvex quadratic function over a ball, is a key subproblem in trust-region methods for solving nonlinear optimization problems. It en…
SDP Duals without Duality Gaps for a Class of Convex Minimax Programs
V. Jeyakumar, J. Vicente-Perez
In this paper we introduce a new dual program, which is representable as a semi-definite linear programming problem, for a primal convex minimax programming model problem and show…
Robust SOS-Convex Polynomial Programs: Exact SDP Relaxations
V. Jeyakumar, G. Li, J. Vicente-Perez
This paper studies robust solutions and semidefinite linear programming (SDP) relaxations of a class of convex polynomial programs in the face of data uncertainty. The class of con…
Convergence of the Lasserre Hierarchy of SDP Relaxations for Convex Polynomial Programs without Compactness
V. Jeyakumar, T. S. Pham, G. Li
The Lasserre hierarchy of semidefinite programming (SDP) relaxations is an effective scheme for finding computationally feasible SDP approximations of polynomial optimization over…
On Polynomial Optimization over Non-compact Semi-algebraic Sets
Vaithilingam Jeyakumar, Jean-Bernard Lasserre, G. Li
We consider the class of polynomial optimization problems for which the quadratic module generated by the polynomials that define and the polynomial $c-f…