Abstract: After developing necessary background theory, the original primal and dual are specified, and the invariant primal and dual LP's are defined. Pairs of linear mappings are defined which establish an effectively one-to-one correspondences between solutions to the original and invariant problems. The invariant problems are recast as a fixed-point problem and precise solution conditions for the fixed-point problem are found. The fixed-point problem is solved by asymptotic and terminating methods; operational conditions for the solution of convex programs, alternative to the Kuhn-Tucker conditions, are developed.
Optimization by the Fixed-Point Method monograph217.pdf by Jalaluddin Abdullah !6 March 2016.