‎A full Nesterov-Todd (NT) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using Euclidean Jordan algebra‎. ‎Two types of‎ ‎full NT-steps are used‎, ‎feasibility steps and centering steps‎. ‎The‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

We consider the extension of primal dual interior point methods for linear programming on symmetric cones, to a wider class of problems that includes approximate necessary optimality conditions for functions expressible as the difference of two convex functions of a special form. Our analysis applies the Jordan-algebraic approach to symmetric cones. As the basic method is local, we apply the id...

Self–scaled barrier functions are fundamental objects in the theory of interior–point methods for linear optimization over symmetric cones, of which linear and semidefinite programming are special cases. We are classifying all self–scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with...

We study the continuous trajectories for solving monotone nonlinear mixed complementarity problems over symmetric cones. While the analysis in [5] depends on the optimization theory of convex log-barrier functions, our approach is based on the paper of Monteiro and Pang [17], where a vast set of conclusions concerning continuous trajectories is shown for monotone complementarity problems over t...

A duality theorem for a pair of Wolfe-type second-order minimax mixed integer symmetric dual programs over cones is proved under separability and η-bonvexity/η-boncavity of the function k(x, y) appearing in the objective, where : . n m k R R R × ֏ Mond-Weir type symmetric duality over cones is also studied under η-pseudobonvexity/ηpseudoboncavity assumptions. Self duality (when the dual proble...

Self{scaled barrier functions are fundamental objects in the theory of interior{point methods for linear optimization over symmetric cones, of which linear and semideenite programming are special cases. We are classifying all self{scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with ...