TY - JOUR
T1 - Solving continuous min-max problems by an iterative entropic regularization method
AU - Sheu, R. L.
AU - Lin, J. Y.
N1 - Funding Information:
1This research work was partially supported by the National Science Council of Taiwan under Project NSC 89-2115-M-006-009. 2The authors thank Professor Paul Tseng and two anonymous referees for valuable comments and suggestions. 3Professor, Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan. 4PhD Candidate, Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan.
PY - 2004/6
Y1 - 2004/6
N2 - We propose a method of outer approximations, with each approximate problem smoothed using entropic regularization, to solve continuous min-max problems. By using a well-known uniform error estimate for entropic regularization, convergence of the overall method is shown while allowing each smoothed problem to be solved inexactly. In the case of convex objective function and linear constraints, an interior-point algorithm is proposed to solve the smoothed problem inexactly. Numerical examples are presented to illustrate the behavior of the proposed method.
AB - We propose a method of outer approximations, with each approximate problem smoothed using entropic regularization, to solve continuous min-max problems. By using a well-known uniform error estimate for entropic regularization, convergence of the overall method is shown while allowing each smoothed problem to be solved inexactly. In the case of convex objective function and linear constraints, an interior-point algorithm is proposed to solve the smoothed problem inexactly. Numerical examples are presented to illustrate the behavior of the proposed method.
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U2 - 10.1023/B:JOTA.0000037605.19435.63
DO - 10.1023/B:JOTA.0000037605.19435.63
M3 - Article
AN - SCOPUS:4444297543
SN - 0022-3239
VL - 121
SP - 597
EP - 612
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 3
ER -