An algorithm for a class of split feasibility problems: application to a model in electricity production

We propose a projection algorithm for solving split feasibility problems involving paramonotone equilibria and convex optimization. The proposed algorithm can be considered as a combination of the projection ones for equilibrium and convex optimization problems. We apply the algorithm for finding an equilibrium point with minimal environmental cost for a model in electricity production. Numerical results for the model are reported.

[1]  Yair Censor,et al.  Algorithms for the Split Variational Inequality Problem , 2010, Numerical Algorithms.

[2]  Y. Censor,et al.  A unified approach for inversion problems in intensity-modulated radiation therapy , 2006, Physics in medicine and biology.

[3]  G. M. Korpelevich The extragradient method for finding saddle points and other problems , 1976 .

[4]  A. Iusem On some properties of paramonotone operators. , 1998 .

[5]  H. Nikaidô,et al.  Note on non-cooperative convex game , 1955 .

[6]  Shih-sen Chang,et al.  A strong convergence theorem for equilibrium problems and split feasibility problems in Hilbert spaces , 2014 .

[7]  C. Byrne,et al.  A unified treatment of some iterative algorithms in signal processing and image reconstruction , 2003 .

[8]  Abdellatif Moudafi,et al.  Split Monotone Variational Inclusions , 2011, J. Optim. Theory Appl..

[9]  Massimo Pappalardo,et al.  Existence and solution methods for equilibria , 2013, Eur. J. Oper. Res..

[10]  C. Byrne,et al.  Iterative oblique projection onto convex sets and the split feasibility problem , 2002 .

[11]  Y. Censor,et al.  The multiple-sets split feasibility problem and its applications for inverse problems , 2005 .

[12]  J. Strodiot,et al.  On extragradient-viscosity methods for solving equilibrium and fixed point problems in a Hilbert space , 2015 .

[13]  Hong-Kun Xu,et al.  Solving the split feasibility problem without prior knowledge of matrix norms , 2012 .

[14]  Yair Censor,et al.  A multiprojection algorithm using Bregman projections in a product space , 1994, Numerical Algorithms.

[15]  Heinz H. Bauschke,et al.  Convex Analysis and Monotone Operator Theory in Hilbert Spaces , 2011, CMS Books in Mathematics.

[16]  J. Krawczyk,et al.  Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets , 2004, IEEE Transactions on Power Systems.

[17]  Abdellatif Moudafi,et al.  Solving proximal split feasibility problems without prior knowledge of operator norms , 2014, Optim. Lett..

[18]  Y. Censor,et al.  Iterative Projection Methods in Biomedical Inverse Problems , 2008 .

[19]  Susana Scheimberg,et al.  An inexact subgradient algorithm for Equilibrium Problems , 2011 .

[20]  Abdellatif Moudafi,et al.  The split common fixed-point problem for demicontractive mappings , 2010 .

[21]  Le Dung Muu,et al.  Iterative methods for solving monotone equilibrium problems via dual gap functions , 2012, Comput. Optim. Appl..

[22]  Yair Censor,et al.  The Split Common Fixed Point Problem for Directed Operators. , 2010, Journal of convex analysis.

[23]  Le Dung Muu,et al.  A hybrid subgradient algorithm for nonexpansive mappings and equilibrium problems , 2014, Optim. Lett..

[24]  Satit Saejung,et al.  On split common fixed point problems , 2014 .

[25]  W. Oettli,et al.  From optimization and variational inequalities to equilibrium problems , 1994 .