**Research Professor, Ph. D.,
D. Sc.(Wales)**

Department of Mathematics

The

Shatin, New Territories, Hong Kong

Office : (852) 3943
7968

Fax :
(852) 2603 5154

E-mail :
kfng@math.cuhk.edu.hk

Functional
Analysis and Optimization, Convex Analysis.

K. F. Ng, "An Open Mapping Theorem", Math. Proc. Camb. (old name of the Journal: Proc. Camb. Phil. Soc.), 74 (1973), 61-66. (PDF file)

C. C. Chou, K. F. Ng
and J. S. Pang, "Minimizing and Stationary Sequences of Constrained
Optimization Problems", SIAM Journal on Control and Optimization, 36
(1998), 1908-1936, *available
at epubs.siam.org.*

L. R. Huang, K. F. Ng and J. P.
Penot, "On Minimizing and Critical Sequences in Nonsmooth
Optimization", SIAM Journal on Optimization, 10 (2000), 999-1019, *available at epubs.siam.org.*

K. F. Ng and X. Y. Zheng,
"Global Error Bounds with Fractional Exponents", Mathematical
Programming, Ser. B88 (2000), 357-370. (DVI file), *available at http://www.springerlink.com/openurl.asp?genre=article&issn=0025-5610&volume=88&issue=2&spage=357.*

K. F. Ng and X. Y. Zheng,
"Error Bounds For Lower Semicontinuous Functions in Normed Spaces", SIAM Journal on Optimization, 12 (2001), 1-17. (DVI file), *available at epubs.siam.org.*

Y. R. He and K. F. Ng, "Best Approximation and Perturbation Property in Hilbert Spaces," J. Optim. Theory App., 126 (2005), No. 2, 265-285. (PS file)

K. F. Ng and X. Y. Zheng,
"Existence of Efficient Points in Vector Optimization and Generalized
Bishop-Phelps Theorem", J. Optim. Theory App., 115 (2002), 29-47. (DVI file), *available at springerlink.metapress.com.*

K. F. Ng and X.Y. Zheng,
"Error Bounds of Constrained Quadratic Functions and Piecewise Affine
Inequality Systems," J. Optim. Theory App., 118 (2003), 584-607.(DVI file), *available at springerlink.metapress.com.*

Kung Fu Ng and Wei Hong Yang,
"Error Bounds for Abstract Linear Inequality Systems", SIAM Journal on Optimization, 13 (2002), 24-43. (DVI file), *available at epubs.siam.org.*

Kung Fu Ng and Wei Hong Yang,
"Regularities and Their Relations to Error Bounds", Math. Program.
Ser. A, 99(2004), 521-538. (PDF file), *available at springerlink.metapress.com.*

Kung Fu Ng and Xi Yin Zheng,
"Characterization of Error Bounds for Convex Multifunctions on Banach
Spaces", Math. Oper. Res., 29(2004), 45-63. ( DVI file) , *available at proquest.umi.com.*

L.R. Huang and K.F. Ng, "On
First and Second-Order Conditions for Error Bounds", SIAM Journal on
Optimization, 14(2004), 1057-1073.(DVI file), *available at epubs.siam.org.*

K. F. Ng and Xi Yin Zheng, "Hoffman's Least Error Bounds for Systems of Linear Inequality", J. Global Optim., 30(2004), 391-403. (DVI file)

Chong Li and K. F. Ng,
"Constraint Qualification, the Strong CHIP and Best Approximation with
Convex Constraints in Banach Spaces", SIAM Journal on Optimization,
14(2003) 584-607, *available
at epubs.siam.org.*

Chong Li and K.F. Ng, ôOn Constraint
Qualification for an Infinite System of Convex Inequalities in a Banach Space?
SIAM Journal on Optimization, 15(2005), No. 2, 488-512. *Available at epubs.siam.org.*

Xin Yi Zheng and K. F. Ng,
"Error Bound Moduli for Conic Convex Systems on Banach Spaces", Math.
Oper. Res., 29(2004), 213-228. *Abstract a**vailable at proquest.umi.com.*

Xin Yi Zheng and K. F. Ng,
"Metric Regularity and Constraint Qualifications for Convex Inequalities
on Banach Spaces", SIAM Journal on Optimization, 14(2004), 757-772, *available at epubs.siam.org.*

K. F. Ng and Wei Hong Yang, "Error Bounds for Some Convex Functions and Distance Composite Functions", SIAM Journal on Optimization, 15(2005), No. 4, 1042-1056. (DVI file)

Chong Li and K. F. Ng, "Strong CHIP for Infinite System of Closed Convex Sets in Normed Linear Spaces", SIAM Journal on Optimization, 16(2005), No. 2, 311-340. (DVI file)

Chong Li and K. F. Ng, "On Best Restricted Range Approximation in Continuous Complex-Valued Function Spaces", Journal of Approximation Theory, 136(2005), issue 2, 159-181. (DVI file)

X. Y. Zheng and K. F. Ng, "The Fermat Rule for Multifunctions in Banach Spaces", Math. Program. Ser. A, 104(2005), 69-90.(PDF file)

"Linear Regularity and f-Regularity of Nonconvex Sets", J. Math. Anal. Appl. 328(2007),257-280, (with R. Zang).

"D-Gap Functions for Nonsmooth Variational Inequality Problems", J. Optim. Theory Appl. doi 10.1007 / s10957-007-9193-1 (2007), (with L. L. Tan).

"Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems", Math. Prog. Ser. A, 110 (2007), 405-429, (with L. L. Tan).

"The Lagrange Multilizer Rule for Multifunctions in Banach Spaces", SIAM J. Optim. 17 (2006), pp. 1154 - 1175., (with X. Y. Zheng) (PDF file)

"Majoring functions and convergence of Gauss-Newton's method for convex composite optimization", SIAM J. Optim., 18 (2007), 613-642, (with C. Li) (PDF file)

"Metric subregularity and constraint qualifications for convex generalized equations in Banach spaces", SIAM J. Optim., 18 (2007), 437-460, (with X.Y. Zheng) (PDF file)

"The SECQ, linear regularity and the strong CHIP for infinite system of closed convex sets in normed linear space", SIAM J. Optim., 18 (2007), 643-665, (with C. Li and T.K. Pong) (PDF file)

"Linear regularity for a collection of subsmooth sets in Banach spaces", SIAM J. Optim., 19(2008), 62-79, (with X.Y. Zheng) (PDF file)

"Unified approach to some geometric results in variational analysis", Journal of Functional Analysis, 248 (2007), 317-343,(with G.Y. Li and X.Y. Zheng) (PDF file)

"Constraint Qualifications for Convex Inequality Systems with Applications in Constrained Optimization", SIAM J. Optim., 19(2008), 163-187, (with C. Li and T.K. Pong) (PDF file)

"On extension of Fenchel duality and its application", SIAM J. Optim., 19(2008), 1489-1509, (with G.Y. Li) (PDF file)

"Merit functions in vector optimization", Math. Program., Ser. A (2008), 1436-4646, (with C.G. Liu and W.H. Yang)

"Restricted weak upper semi-continuity of subdifferentials of convex functions on Banach spaces", set-valued Analysis, 16(2008), 245-255, (with X.Y. Zheng)

"Calmness For L-Subsmooth Multifunctions in Banach Spaces", SIAM J. Optim., 19(2008), 1648-1673, (with X.Y. Zheng) (PDF File)

"Error Bounds of Generalized D-gap Functions for Nonsmooth and Nonmonotone Variational Inequality Problems", SIAM J. Optim., 20(2009), 667-690, (with G.Y. Li) (PDF File)

"Strong KKT Conditions and Weak Sharp Solutions in Convex-Composite Optimization", Math. Programming, Series A, 126 (2010), 259-279. (with X.Y. Zheng) (PDF File)

"Constraint Qualifications for Extended Farkas's Lemma and Lagrangian Dualities in Convex Infinite Programming", SIAM J. Optim., 20(2009), 1311-1332, (with D.H. Fang and C. Li) (PDF File)

"Metric Subregularity and Calmness for Nonconvex Generalized Equations in Banach Spaces", SIAM J. Optim., 20(2010), 2119-2136, (with X. Y. Zheng) (PDF File)

"A unified separation theorem for closed sets in a Banach space and optimality conditions for vector optimization", SIAM J. Optim., 21(2011), 886-911, (with X. Y. Zheng) (PDF File)

"Subdifferential calculus rules for supremum functions in convex analysis", SIAM J. Optim., 21(2011), 782-797, (with C. Li) (PDF File)

"Metric subregularity for proximal generalized equations in Hilbert spaces", Nonlinear Anal., Volume 75, issue 3 (2012), p. 1686-1699. (with X. Y. Zheng) (PDF File)

"Ekeland's variational principle for set-valued functions", SIAM J. Optim., 21(2011), 41-56. (with C.G. Liu) (PDF File)

"Subsmooth semi-infinite and infinite optimization problems", Math. Programming, Series A, 134(2012), 365-393, DOI : 10.1007/s10107-011-0440-8. (with X. Y. Zheng) (PDF File)

"Convergence analysis of the Gauss-Newton method for convex inclusion and convex-composite optimization problems", J. Math. Anal. Appl., Volume 389, Issue 1, (2012), p. 469-485. (with C. Li) (PDF File)

"Approximate Solutions for Abstract Inequality Systems", SIAM J. Optim., 23(2013), no. 2, 1237-1256., (with C. Li)

"Comments on: Farkas’ lemma: three decades of generalizations for mathematical optimization", TOP, 22 (2014), no. 1, 23-26. (with C. Li) (PDF file)

"Metric Subregularity of Piecewise Linear Multifunctions and Applications to Piecewise Linear Multiobjective Optimization", SIAM J. Optim., 24 (2014), no. 1, 154-174. (with X. Y. Zheng) (PDF file)

"Hölder weak sharp minimizers and Hölder tilt-stability", Nonlinear Anal., 120 (2015), 186-201. (with X. Y. Zheng) (PDF file)

"Hölder stable minimizers, tilt stability and Hölder metric regularity of subdifferentials", SIAM J. Optim., 25 (2015), no. 1, 416-438. (with X. Y. Zheng) (PDF file)

"Extended Newton methods for conic inequalities: Approximate solutions and the extended Smale α-theory", J. Math. Anal. Appl., 440 (2016), p. 636-660. (with C. Li) (PDF File)

"Stability of *p*-Order Metric Regularity", Vietnam J. Math., Volume 46, Issue 2 (2018), p. 285-291. (with Y.R. He) *Available at
link.springer.com*.

"Second order sufficient conditions for stable well-posedness of ϕ prox-regular functions, Pure and Applied Functional Analysis, Special issue on Control, Optimization and Variational Analysis, Volume 4 (2019), Number 1, 137-150. (with X.Y. Zheng and J.X. Zhu)

"Fully Hölderian Stable Minimum with Respect to Both Tilt and Parameter Perturbation", SIAM J. Optim., 28-3 (2018), pp. 2601-2624. (with X.Y. Zheng and J.X. Zhu) (PDF file)

"Quantitative Analysis for Perturbed Abstract Inequality Systems in Banach Spaces, SIAM Journal on Optimization, Volume 28 (2018), No. 4, pp.2872-2901. (with C. Li) (PDF File)

"Differentiability of Convex Functions in a Locally Convex Topological Vector Spaces, Journal of Convex Analysis, to appear in 26 (2019) (with X. Y. Zheng) (PDF File)

"Stability of error bounds for conic subsmooth inequalities", ESAIM: Control, Optimisation and Calculus of Variations, 2018, DOI: https://doi.org/10.1051/cocv/2018047 (with X. Y. Zheng)