316 citations · 903 across the 32 of their papers we have counts for
33 papers
Radial-type error bounds for semidefinite feasibility problems without strict feasibility: qualitative estimates and asymptotic tightness
Mitsuhiro Nishijima, Guoyin Li, Bruno F. Lourenço
In this paper, we develop a systematic framework for deriving explicit error bounds for semidefinite feasibility problems without assuming strict feasibility (Slater's condition),…
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…
A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems
Tan Nhat Pham, Minh N. Dao, Rakibuzzaman Shah +3
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex f…
Frank-Wolfe-type methods for a class of nonconvex inequality-constrained problems
Liaoyuan Zeng, Yongle Zhang, Guoyin Li +2
The Frank-Wolfe (FW) method, which implements efficient linear oracles that minimize linear approximations of the objective function over a fixed compact convex set, has recently r…
Retraction-based first-order feasible methods for difference-of-convex programs with smooth inequality and simple geometric constraints
Yongle Zhang, Guoyin Li, Ting Kei Pong +1
In this paper, we propose first-order feasible methods for difference-of-convex (DC) programs with smooth inequality and simple geometric constraints. Our strategy for maintaining…
Inertial Proximal Block Coordinate Method for a Class of Nonsmooth Sum-of-Ratios Optimization Problems
Radu Ioan Boţ, Minh N. Dao, Guoyin Li
In this paper, we consider a class of nonsmooth sum-of-ratios fractional optimization problems with block structure. This model class is ubiquitous and encompasses several importan…
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…
Extrapolated Proximal Subgradient Algorithms for Nonconvex and Nonsmooth Fractional Programs
Radu Ioan Boţ, Minh N. Dao, Guoyin Li
In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, where the numerator can be written as the sum of a continuously differentiable convex funct…
Efficiently Maximizing a Homogeneous Polynomial over Unit Sphere without Convex Relaxation
Yuning Yang, Guoyin Li
This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenva…
Kurdyka-Łojasiewicz exponent via inf-projection
Peiran Yu, Guoyin Li, Ting Kei Pong
Kurdyka-Lojasiewicz (KL) exponent plays an important role in estimating the convergence rate of many contemporary first-order methods. In particular, a KL exponent of for…
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…
SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization
N. H. Chieu, J. W. Feng, W. Gao +2
In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. Th…
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…
Calculus of the exponent of Kurdyka-Łojasiewicz inequality and its applications to linear convergence of first-order methods
Guoyin Li, Ting Kei Pong
In this paper, we study the Kurdyka-Łojasiewicz (KL) exponent, an important quantity for analyzing the convergence rate of first-order methods. Specifically, we develop various cal…
Finding the maximum eigenvalue of a class of tensors with applications in copositivity test and hypergraphs
Haibin Chen, Yannan Chen, Guoyin Li +1
Finding the maximum eigenvalue of a symmetric tensor is an important topic in tensor computation and numerical multilinear algebra. This paper is devoted to a semi-definite program…
Convergence rate analysis for averaged fixed point iterations in the presence of Hölder regularity
Jonathan M. Borwein, Guoyin Li, Matthew K. Tam
In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under a bounded…
Error Bounds for Parametric Polynomial Systems with Applications to Higher-Order Stability Analysis and Convergence Rates
G. Li, B. S. Mordukhovich, T. T. A. Nghia +1
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many p…
Peaceman-Rachford splitting for a class of nonconvex optimization problems
Guoyin Li, Tianxiang Liu, Ting Kei Pong
We study the applicability of the Peaceman-Rachford (PR) splitting method for solving nonconvex optimization problems. When applied to minimizing the sum of a strongly convex Lipsc…
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…
Further Results on Cauchy Tensors and Hankel Tensors
Haibin Chen, Guoyin Li, Liqun Qi
In this article, we present various new results on Cauchy tensors and Hankel tensors. { We first introduce the concept of generalized Cauchy tensors which extends Cauchy tensors in…
Positive Semi-Definiteness of Generalized Anti-Circulant Tensors
Guoyin Li, Liqun Qi, Qun Wang
Anti-circulant tensors have applications in exponential data fitting. They are special Hankel tensors. In this paper, we extend the definition of anti-circulant tensors to generali…
SOS-Hankel Tensors: Theory and Application
Guoyin Li, Liqun Qi, Yi Xu
Hankel tensors arise from signal processing and some other applications. SOS (sum-of-squares) tensors are positive semi-definite symmetric tensors, but not vice versa. The problem…
New Classes of Positive Semi-Definite Hankel Tensors
Qun Wang, Guoyin Li, Liqun Qi +1
A Hankel tensor is called a strong Hankel tensor if the Hankel matrix generated by its generating vector is positive semi-definite. It is known that an even order strong Hankel ten…