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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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초록· 키워드
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A globally convergent algorithm for solving equilibrium problems is proposed. The algorithm is based on a proximal point algorithm (shortly (PPA)) with a positive definite matrix M which is not necessarily symmetric. The proximal function in existing (PPA) usually is the gradient of a quadratic function, namely, ${\nabla}({\parallel}x{\parallel}^2_M)$. This leads to a proximal point-type algorithm. We first solve pseudomonotone equilibrium problems without Lipschitzian assumption and prove the convergence of algorithms. Next, we couple this technique with the Banach contraction method for multivalued variational inequalities. Finally some computational results are given.
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참고문헌 (18)
참고문헌 신청
A. Auslender / 1999 / A logarithmic-quadratic proximal method for variational inequalities / Comput. Optim. Appl 12 (1) : 31 ~ 40
A. Moudafi / 1999 / Proximal point algorithm extended to equilibrium problem / J. Nat. Geom 15 (1) : 91 ~ 100
B. S. He / 2009 / Proximal-point algorithm using a linear proximal term / J. Optim. Theory Appl 141 (2) : 299 ~ 319
E. Blum / 1994 / From optimization and variational inequality to equilibrium problems / Math. Student 63 (1) : 123 ~ 145
F. Facchinei / 2003 / Finite-Dimensional Variational Inequalities and Comple- mentary Problems Vol. I, II / Springer-Verlag
A. Moudafi / 1999 / Proximal point algorithm extended to equilibrium problem / J. Nat. Geom 15 (1) : 91 ~ 100
B. S. He / 2009 / Proximal-point algorithm using a linear proximal term / J. Optim. Theory Appl 141 (2) : 299 ~ 319
E. Blum / 1994 / From optimization and variational inequality to equilibrium problems / Math. Student 63 (1) : 123 ~ 145
F. Facchinei / 2003 / Finite-Dimensional Variational Inequalities and Comple- mentary Problems Vol. I, II / Springer-Verlag
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