Isotonicity of the metric projection with respect to the mutually dual orders and complementarity problems

[1]  O. P. Ferreira,et al.  On the Spherical Quasi-convexity of Quadratic Functions on Spherically Subdual Convex Sets , 2018, Journal of Optimization Theory and Applications.

[2]  Yonghong Wu,et al.  Characterization of the Cone and Applications in Banach Spaces , 2019, Numerical Functional Analysis and Optimization.

[3]  S. Z. N'emeth,et al.  Conic optimization and complementarity problems , 2016, 1607.05161.

[4]  S. Z. N'emeth,et al.  Isotone projection cones and Q-matrices , 2016, 1608.06958.

[5]  João X. da Cruz Neto,et al.  The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem , 2018, SIAM J. Optim..

[6]  O. P. Ferreira,et al.  Generalized isotone projection cones , 2012 .

[7]  S. Z. N'emeth A duality between the metric projection onto a convex cone and the metric projection onto its dual in Hilbert spaces , 2012, 1212.5438.

[8]  Pedro Gajardo,et al.  Equilibrium problems involving the Lorentz cone , 2014, J. Glob. Optim..

[10]  Sandor Z. Németh,et al.  Extended Lorentz cones and mixed complementarity problems , 2014, J. Glob. Optim..

[11]  Sandor Z. Németh,et al.  Extended Lorentz Cones and Variational Inequalities on Cylinders , 2016, J. Optim. Theory Appl..

[12]  Sandor Nemeth,et al.  A duality between the metric projection onto a convex cone and the metric projection onto its dual , 2012 .

[13]  A. B. N'emeth,et al.  Self-dual cones, generalized lattice operations and isotone projections , 2012 .

[14]  Guoping He,et al.  A globally and quadratically convergent smoothing Newton method for solving second-order cone optimization , 2015 .

[15]  Efe A. Ok,et al.  Optimal solutions to variational inequalities on Banach lattices , 2012 .

[16]  Mujahid Abbas,et al.  Isotone Projection Cones and Nonlinear Complementarity Problems , 2014 .

[17]  Mujahid Abbas,et al.  Solving nonlinear complementarity problems by isotonicity of the metric projection , 2012 .

[18]  Orizon Pereira Ferreira,et al.  Generalized projections onto convex sets , 2012, J. Glob. Optim..

[19]  J. Jahn,et al.  General theorems of the alternative in variable ordering structures , 2021, Journal of Nonlinear and Variational Analysis.

[20]  Jinlu Li The Solvability of Nonlinear Split Ordered Variational Inequality Problems in Partially Ordered Vector Spaces , 2018, Numerical Functional Analysis and Optimization.

[21]  C. S. Lalitha,et al.  Scalarizations for a unified vector optimization problem based on order representing and order preserving properties , 2018, J. Glob. Optim..

[22]  Sandor Z. Németh,et al.  Linear Complementarity Problems on Extended Second Order Cones , 2017, Journal of Optimization Theory and Applications.

[23]  Mujahid Abbas,et al.  Finding solutions of implicit complementarity problems by isotonicity of the metric projection , 2012 .

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

[25]  H. H. Schaefer Banach Lattices and Positive Operators , 1975 .

[26]  Yonghong Wu,et al.  Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities , 2017, J. Optim. Theory Appl..

[27]  L. F. Prudente,et al.  A semi-smooth Newton method for projection equations and linear complementarity problems with respect to the second order cone , 2016 .

[28]  Lishan Liu,et al.  The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces , 2015 .

[29]  G. Isac,et al.  Monotonicity of metric projections onto positive cones of ordered Euclidean spaces , 1986 .

[30]  Yonghong Wu,et al.  Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces , 2017, J. Optim. Theory Appl..

[31]  Orizon Pereira Ferreira,et al.  How to project onto extended second order cones , 2016, Journal of Global Optimization.

[32]  Orizon Pereira Ferreira,et al.  Projection onto simplicial cones by a semi-smooth Newton method , 2015, Optim. Lett..

[33]  Miek Messerschmidt,et al.  Normality of spaces of operators and quasi-lattices , 2013, 1307.1415.