Preface

Christian Kanzow; Dong-Hui Li; Nobuo Yamashita

doi:10.3934/naco.2011.1.1i

Article Contents

2011, Volume 1, Issue 1: i-v. Doi: 10.3934/naco.2011.1.1i open access

This issue Previous Article Next Article On methods for solving nonlinear semidefinite optimization problems

Preface

1.
University of Würzburg, Institute of Mathematics, Am Hubland, 97074 Würzburg
2.
School of Mathematical Sciences, South China Normal University, Guangzhou, 510631
3.
Graduate School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, 606-8501

Published: January 2011

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Abstract

It is our great pleasure and honor to dedicate the first issue of “Numerical Algebra, Control and Optimization” to Professor Masao Fukushima on the occasion of his 60th birthday. The papers contributed to this issue have been written by his old friends, colleagues and former students, and bring up various topics on optimization, which represent Professor Fukushima's wide-ranging interest in all aspects of optimization.

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References

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[28]	M. Fukushima, Parallel variable transformation in unconstrained optimization, SIAM Journal on Optimization, 8 (1998), 658-672.doi: 10.1137/S1052623496309879.
[29]	M. Fukushima and J. S. Pang, Some feasibility issues in mathematical programs with equilibrium constraints, SIAM Journal on Optimization, 8 (1998), 673-681.doi: 10.1137/S105262349731577X.
[30]	C. Kanzow and M. Fukushima, Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities, Mathematical Programming, 83 (1998), 55-87.doi: 10.1007/BF02680550.
[31]	J.-S. Pang and M. Fukushima, Complementarity constraint qualifications and simplified B-stationarity conditions for mathematical programs with equilibrium constraints, Computational Optimization and Applications, 13 (1999), 111-136.doi: 10.1023/A:1008656806889.
[32]	X. Chen and M. Fukushima, Proximal quasi-Newton methods for nondifferentiable convex optimization, Mathematical Programming, 85 (1999), 313-334.doi: 10.1007/s101070050059.
[33]	M. Fukushima and J. S. Pang, Convergence of a smoothing continuation method for mathematical programs with complementarity constraints, in "Ill-posed Variational Problems and Regularization Techniques" (eds. M. Thera and R. Tichatschke), Lecture Notes in Economics and Mathematical Systems, 477 (1999), Springer-Verlag, Berlin/Heidelberg, 99-110.
[34]	N. Yamashita and M. Fukushima, The proximal point algorithm with genuine superlinear convergence for the monotone complementarity problem, SIAM Journal on Optimization, 11 (2001), 364-379.doi: 10.1137/S105262349935949X.
[35]	D. Li and M. Fukushima, On the global convergence of the BFGS method for nonconvex unconstrained optimization problems, SIAM Journal on Optimization, 11 (2001), 1054-1064.doi: 10.1137/S1052623499354242.
[36]	M. Fukushima, Z.-Q. Luo and P. Tseng, Smoothing functions for second-order-cone complementarity problems, SIAM Journal on Optimization, 12 (2001), 436-460.doi: 10.1137/S1052623400380365.
[37]	M. Fukushima and P. Tseng, An implementable active-set algorithm for computing a B-stationary point of the mathematical program with linear complementarity constraints, SIAM Journal on Optimization, 12 (2002), 724-739. [Erratum,doi: 10.1137/S1052623499363232.
[38]	M. Fukushima, Z.-Q. Luo and P. Tseng, A sequential quadratically constrained quadratic programming method for differentiable convex minimization, SIAM Journal on Optimization, 13 (2003), 1098-1119.doi: 10.1137/S1052623401398120.
[39]	J.-S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games, Computational Management Science, 2 (2005), 21-56. [Erratum,doi: 10.1007/s10287-004-0010-0.
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[41]	X. Chen and M. Fukushima, Expected residual minimization method for stochastic linear complementarity problems, Mathematics of Operations Research, 30 (2005), 1022-1038.doi: 10.1287/moor.1050.0160.
[42]	P. Zhong and M. Fukushima, Second order cone programming formulations for robust multi-class classification, Neural Computation, 19 (2007), 258-282.doi: 10.1162/neco.2007.19.1.258.
[43]	M. Fukushima, A class of gap functions for quasi-variational inequality problems, Journal of Industrial and Management Optimization, 3 (2007), 165-171.
[44]	M. A. Majig, A. R. Hedar and M. Fukushima, Hybrid evolutionary algorithm for solving general variational inequality problems, Journal of Global Optimization, 38 (2007), 637-651.doi: 10.1007/s10898-006-9102-4.
[45]	H. Fang, X. Chen and M. Fukushima, Stochastic $R_0$ matrix linear complementarity problems, SIAM Journal on Optimization, 18 (2007), 482-506.doi: 10.1137/050630805.
[46]	G. H. Lin, X. Chen and M. Fukushima, Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization, Mathematical Programming, 116 (2009), 343-368.doi: 10.1007/s10107-007-0119-3.
[47]	X. Chen, C. Zhang and M. Fukushima, Robust solution of monotone stochastic linear complementarity problems, Mathematical Programming, 117 (2009), 51-80.doi: 10.1007/s10107-007-0163-z.
[48]	C. Kanzow, I. Ferenczi and M. Fukushima, On the local convergence of semismooth Newton methods for linear and nonlinear second-order cone programs without strict complementarity, SIAM Journal on Optimization, 20 (2009), 297-320.doi: 10.1137/060657662.
[49]	S. S. Zhu and M. Fukushima, Worst-case conditional Value-at-Risk with application to robust portfolio management, Operations Research, 57 (2009), 1155-1168.doi: 10.1287/opre.1080.0684.
[50]	G. H. Lin and M. Fukushima, Stochastic equilibrium problems and stochastic mathematical programs with equilibrium constraints: A survey, Pacific Journal of Optimization, 6 (2010), 455-482.