Convex Analysis

[C1] Borwein, J.M.; Li, Guoyin; Tam, Mattew, Convergence rate analysis for averaged fixed point iterations in the presence of Holder regularity, to appear in SIAM Journal on Optimization , PDF Download

[C2] Drusvyatskiy, D., Li, Guoyin; Wolkowicz, H., A note on alternating projections for ill-posed semidefinite feasibility problems, to appear in Math. Program. Ser. A, , PDF Download

[C3] Borwein, J.M.; Li, Guoyin; Yao, Liangjin, Analysis of the convergence rate for the cyclic projection algorithm applied to basic semi-algebraic convex sets, to appear in SIAM Journal on Optimization, , PDF Download

[C4] Li, Guoyin, Global Error Bounds for Piecewise Convex Polynomials, Accepted by Mathematical Programming,. PDF Download

[C5] Jeyakumar, V.; Li, Guoyin, Exact SDP Relaxations for Classes of Nonlinear Semidefinite Programming Problems, accepted by: Operation Research Letters PDF Download

[C6] Li, Guoyin, On the asymptotic well behaved functions and global error bound for convex polynomials , accepted by: SIAM Journal on Optimization, 20(2010), No. 4, 1923-1943, PDF Download

[C7] Li, Guoyin; Ng, Kung Fu, On extension of Fenchel duality and its application, SIAM Journal on Optimization, 19 (2008), 1489-1509. PDF Download

[C8] Jeyakumar, V.; Li, Guoyin, New strong duality results for convex programs with separable constraints, to appear in European Journal of Operational Research . available online .

[C9] Jeyakumar, V.; Li, Guoyin, Farkas's Lemma for Separable Sublinear Inequalities without Qualifications, accepted by: Optimization Letters , available online

[C10] Jeyakumar, V.; Li, Guoyin, Stable zero duality gaps in convex programming: complete characterizations with applications to semidefinite programs, Journal of Mathematical Analysis and Applications. , available online . .

[C11] Jeyakumar, V.; Li, Guoyin, New dual constraint qualifications characterizing zero duality gaps of convex programs and semidefinite programs. accepted by: Nonlinear Analysis available online . .

[C12] Li, Guoyin; Jeyakumar, V., Qualification-free optimality conditions for convex programs with separable inequality constraints, Journal of Convex analysis , 4 (2009), available online .

[C13] Jeyakumar, V., Li, Guoyin, Wang, Jinhua, Some robust convex programs without a duality gap, accepted by Journal of Convex analysis PDF Download .

Nonsmooth Analysis and Variational Analysis

[V1] Li, Guoyin; B.S. Mordukhovich; Nghia, T. T. A; P.T. Son, Error Bounds for Parametric Polynomial Systems with Applications to Higher-Order Stability Analysis and Convergence Rates, accepted by Mathematical Programming PDF Download

[V2] Li, Guoyin; B.S. Mordukhovich; P.T. Son, New error bounds for nonconvex polynomial systems with applications to Holderian stability in optimization and spectral theory of tensors, accepted by Mathematical Programming PDF Download

[V3] Li, Guoyin; B.S. Mordukhovich, Holder Metric Subregularity with Applications to Proximal Point Method, accepted by SIAM Journal on Optimization PDF Download

[V4] Li, Guoyin; Ng, Kung Fu; Zheng, Xi Yin, Unified approach to some geometric results in variational analysis . , Journal of Functional Analysis, 248 (2007), no. 2, 317--343. PDF Download

[V5] Li, Guoyin, Ng, Kung Fu, Error bounds of generalized D-gap functions for nonsmooth and nonmonotone variational inequality problems , SIAM Journal on Optimization, 20(2009), no. 2, 667-690. PDF Download

[V6] Li, Guoyin; Tang, Chunming; Yu, Gaohang; Wei, Zengxin, On a separation principle for nonconvex sets , Set Valued Analysis 16 (2008), no. 7-8, 851-860.

[V7] Li, Guoyin, Tang, Chunming; Wei, Zengxin, Error Bound Results for Generalized D-gap Functions of Nonsmooth Variational Inequality Problems, accepted by: Journal of Computional Applied Mathematics available online

[V8] Li, Guoyin; T.K. Pong, Douglas-Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems, accepted by Mathematical Programming PDF Download

[V9] Li, Guoyin; T.K. Pong, Global convergence of splitting methods for nonconvex composite optimization, accepted by SIAM Journal on Optimization PDF Download

[V10] Li, Guoyin; T.K. Pong, Calculus of the exponent of Kurdyka-Lojasiewicz inequality and its applications to linear convergence of first-order methods, accepted by Foundations of Computational Mathematics PDF Download

Global Optimization

[G1] Jeyakumar, V,; Li, Guoyin, Exact Second-Order Cone Programming Relaxations for Some Nonconvex Minimax Quadratic Optimization Problems, accepted by SIAM Journal on Optimization PDF Download

[G2] Jeyakumar, V,; Lasserre, J.B.; Li Guoyin; T.S. Pham,Convergent Semidefinite Programming Relaxations for Global Bilevel Polynomial Optimization Problems, accepted by SIAM Journal on Optimization . PDF Download

[G3] Jeyakumar, V,; Li Guoyin, Trust--Region Problems with Linear Inequality Constraints: Exact SDP Relaxation, Global Optimality and Applications, Accepted by Mathematical Programming PDF Download

[G4] Jeyakumar, V,; Li Guoyin, Exact Conic Programming Relaxations for a Class of Convex Polynomial Cone-Programs, Accepted by Journal of Optimization Theory and its Applications PDF Download

[G5] Jeyakumar, V,; Li Guoyin, Lasserre, J.B., On Polynomial Optimization over Non-compact Semi-algebraic Sets, accepted by Journal of Optimization Theory and its Applications . PDF Download

[G6] Jeyakumar, V.; Pham, T.S. and Li Guoyin, Convergence of the Lasserre Hierarchy of SDP Relaxations for Convex Polynomial Programs without Compactness, accepted by Operation Research Letters . PDF Download

[G7] Jeyakumar, V.; Lee, G. M.; Li, Guoyin, Alternative theorems for quadratic inequality systems and global quadratic optimization , SIAM Journal on Optimization 20(2009), no. 2, 983-1001. 20(2009), no. 2, 667-690. PDF Download

[G8] Jeyakumar, V.; Li, Guoyin Necessary global optimality conditions for nonlinear programming with polynomial constraint, Mathematical Programming, available online . PDF Download

[G9] Li, Guoyin, Global Quadratic Minimization over Bivalent Constraints: Necessary and Sufficient Global Optimality Condition, accepted by Journal of Optimization Theory and its Applications . PDF Download

[G10] Jeyakumar, V,; Li Guoyin; Srisatkunaraja S., Global Optimality Principles for Polynomial Optimization Problems over Box or Bivalent Constraints by Separable Polynomial Approximations, UNSW preprint 2012 (Journal of Global Optimization, accepted for publication, 01/03/2013). PDF Download

[G11] Li, Guoyin, A Note on Nonconvex Minimax Theorem involving Separable Homogeneous Polynomials, accepted by Journal of Optimization Theory and its Applications . PDF Download

[G12] Jeyakumar, V.; Li, Guoyin, Regularized Lagrangian duality for linearly constrained quadratic optimization and trust-region problems, Journal of Global Optimization , available online ,

[G13] Jeyakumar, V., Huy N.Q.; Li, Guoyin, Necessary and sufficient conditions for S-lemma and nonconvex quadratic optimization, Optimization and Engineering, available online . PDF Download

[G14] Jeyakumar, V.; Li, Guoyin, Robust Solutions of Quadratic Optimization over Single Quadratic Constraint under Interval Uncertainty, accepted by Journal of Global Optimization available online .

[G15] Jeyakumar, V. Lee, G.M.; Li, Guoyin, Global optimality conditions for classes of nonconvex multi-objective quadratic optimization problems, To appear in the Springer Book Volume dedicated to Professor B. Mordukhovich on his 60th birthday .

[U1] Goberna M.A.; Jeyakumar, V.; Li, Guoyin; Vicente-P\'{e}rez, J., Robust solutions of multi-objective linear semi-infinite programs under constraint data uncertainty, Accepted by SIAM Journal on Optimization . PDF Download

[U2] Goberna M.A.; Jeyakumar, V.; Li, Guoyin; Lopez M.A. Robust linear semi-inifinte programming duality under uncertainty, Accepted by Mathematical Programming . PDF Download

[U3] Jeyakumar, V.; Li, Guoyin, Strong duality in robust convex programming: complete characterizations, to appear in SIAM Journal on Optimization available online .

[U4] Jeyakumar, V.; Li, Guoyin; G.M. Lee., A Robust von Neumann Minimax Theorem for Zero-Sum Games under Bounded Payoff Uncertainty, accepted by Operation Research Letters available online . PDF Download

[U5] Jeyakumar, V.; Li, Guoyin, B.S. Mordukhovich, J.W. Wang, Strong Duality and Nonsmooth Newton Methods for Robust Best Approximation with Interpolation Constraints under Ellipsoidal Uncertainty, accepted by Nonlinear Analysis available online . PDF Download

[U6] Jeyakumar, V.; Li, Guoyin, Robust duality for fractional programming with constraint-wise data uncertainty , Accepted by Journal of Optimization Theory and its Applications

[U7] Jeyakumar, V.; Li, Guoyin; G.M. Lee, Robust duality for generalized convex programming problems under data uncertainty, Accepted by Nonlinear Analysis. PDF Download

[U8] Li, Guoyin,; Jeyakumar, V.; Lee, G. M., Robust conjugate duality for convex optimization under uncertainty and its application to data classification, accepted by Nonlinear Analysis available online . PDF Download

[U9] Jeyakumar, V.; Wang, J.H.,; Li, Guoyin, Lagrange multiplier characterizations of robust best approximations under constraint data uncertainty, accepted by Journal of Mathematical Analysis and Applications. , PDF Download

[U10] Jeyakumar, V.; Li, Guoyin, Robust Farkas' lemma for uncertain linear systems with applications, to appear in Positivity available online . PDF Download .

[U11] Jeyakumar, V.; Li, Guoyin, Characterizing robust set containments and solutions of uncertain linear programs without qualifications, Operation Research Letter , available online .

[U12] Jeyakumar, V.; Li, Guoyin, Strong Duality in Robust Semi-Definite Linear Programming under Data Uncertainty, accepted by Optimization , PDF Download

[U13] Bot, R.I.; Jeyakumar, V.; Li,Guoyin; Robust Duality in Parametric Convex Optimization, accepted by Set-Valued and Variational Analysis , PDF Download

[U14] Jeyakumar, V.; Li,Guoyin; A New Class of Alternative Theorems for SOS-Convex Inequalities and Robust Optimization, accepted by Applicable Analysis , PDF Download

[U15] Li,Guoyin; Ma, Alfred Ka Chun; Pong, Ting Kei: Robust least square semidefinite programming with applications, accepted by Computational Optimization and Applications , PDF Download

[U16] Jeyakumar, V.; G.M. Lee.; Li, Guoyin; Characterizing Robust Solution Sets of Convex Programs under Data Uncertainty, Accepted by Journal of Optimization Theory and its Applications PDF Download

[U17] Jeyakumar, V.; Li, G.; Vicente-Perez, J. Robust SOS-convex polynomial optimization problems: exact SDP relaxations. Optimization Letters, 9 (2015), no. 1, 1-18. PDF Download

[U18] Goberna M.A.; Jeyakumar, V.; Li, Guoyin; Vicente-Perez, J., Robust solutions to multi-objective linear programs with uncertain data, European Journal of Operational Research Volume 242, Issue 3, 1 May 2015, Pages 730-743. PDF Download

Numerical Optimization

[N1] Wei, Zengxin; Li, Guoyin; Qi, Liqun, Global convergence of the Polak-Ribiere-Polyak conjugate gradient method with inexact line searches for nonconvex unconstrained optimization problems , Mathematics of Computation, 77 (2008), 2173-2193. PDF Download

[N2] Li, Guoyin; Tang, Chunming; Wei, Zengxin, New conjugacy condition and related new conjugate gradient methods for unconstrained optimization. , Journal of Computional Applied Mathematics 202 (2007), no. 2, 523--539.

[N3] Tang, Chunming, Jinbao Jian, Li, Guoyin, A working set SQCQP algorithm with simple nonmonotone penalty parameters, accepted by Journal of Computations and Applied Mathematics.

[N4] Yu, Gaohang; Guan, Lutai; Li, Guoyin, Global convergence of modifed Polak-Ribiere-Polyak conjugate gradient methods with sufficient descent property, Journal of Industrial and Management Optimization 4 (2008), No. 3, 565-579 available online

[N5] Jeyakumar, V.; Li, Guoyin; Suthaharan S., Robust support vector machine classifiers with uncertain knowledge sets via robust optimization, accepted by Optimization , PDF Download

[N6] Yuan, Gonglin; Wei Zengxin; Li, Guoyin, A Modified Polak-Ribiere-Polyak Conjugate Gradient Algorithm for Nonsmooth Convex Programs, accepted by Journal of Computional Applied Mathematics , PDF Download

Multilinear Algebra and Tensor Computation

[T1] Hu, Shenglong; Li, Guoyin, Convergence rate analysis for the higher order power method in best rank one approximations of tensors, accepted by Numerische Mathematik PDF Download

[T2] Li, Guoyin; Qi, Liqun; Yu, Gaohang, Semismoothness of the Maximum Eigenvalue Function of a Symmetric Tensor and its Application, to appear in Linear Algebra and its Applications PDF Download

[T3] Li, Guoyin; Qi, Liqun; Yu, Gaohang, The Z-eigenvalues of a Symmetric Tensor and its Application to Spectral Hypergraph Theory, to appear in Numerical Linear Algebra with Applications PDF Download

[T4] Hu, Shenglong; Li, Guoyin; Qi, Liqun; Yisheng Song, Finding the Maximum Eigenvalue of Essentially Nonnegative Symmetric Tensors via Sum of Squares Programming, preprint. to appear in Journal of Optimization Theory and its Applications . PDF Download

[T5] Hu, Shenglong; Li, Guoyin; Qi, Liqun, A Tensor Analogy of Yuan's Theorem of the Alternative and Polynomial Optimization with Sign structure, to appear in Journal of Optimization Theory and its Applications . PDF Download

[T6] Li, Guoyin; Qi, Liqun; Wang Qun, Positive Semi-Definiteness of Generalized Anti-Circular Tensors, to appear in Communications in Mathematical Sciences . PDF Download

[T7] Chen, Haibin, Li, Guoyin; Qi, Liqun, SOS Tensor Decomposition: Theory and Applications, to appear in Communications in Mathematical Sciences . PDF Download