caa a22 4500 463169786 CHVBK 20180406164809.0 cr unu---uuuuu 170326e20070101xx s 000 0 eng 10.1007/s10957-006-9055-2 doi (NATIONALLICENCE)springer-10.1007/s10957-006-9055-2 Lower-Order Penalization Approach to Nonlinear Semidefinite Programming [Elektronische Daten] [X. Huang, X. Yang, K. Teo] In this paper, we reformulate a nonlinear semidefinite programming problem into an optimization problem with a matrix equality constraint. We apply a lower-order penalization approach to the reformulated problem. Necessary and sufficient conditions that guarantee the global (local) exactness of the lower-order penalty functions are derived. Convergence results of the optimal values and optimal solutions of the penalty problems to those of the original semidefinite program are established. Since the penalty functions may not be smooth or even locally Lipschitz, we invoke the Ekeland variational principle to derive necessary optimality conditions for the penalty problems. Under certain conditions, we show that any limit point of a sequence of stationary points of the penalty problems is a KKT stationary point of the original semidefinite program. Springer Science+Business Media, Inc., 2007 Semidefinite programming nationallicence lower-order penalty methods nationallicence Ekeland variational principle nationallicence optimality conditions nationallicence Huang X. Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing, China and School of Management, Fudan University, Shanghai, China aut Yang X. Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong, China aut Teo K. Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia aut Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/1(2007-01-01), 1-20 0022-3239 132:1<1 2007 132 10957 https://doi.org/10.1007/s10957-006-9055-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-006-9055-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Huang X. Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing, China and School of Management, Fudan University, Shanghai, China aut NATIONALLICENCE 700 1- Yang X. Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong, China aut NATIONALLICENCE 700 1- Teo K. Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/1(2007-01-01), 1-20 0022-3239 132:1<1 2007 132 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer