hsd - EE236A (Fall 2007-08) Lecture 15 Self-dual...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EE236A (Fall 2007-08) Lecture 15 Self-dual formulations initialization and infeasibility detection skew-symmetric LPs homogeneous self-dual formulation self-dual formulation 151 Solution of an LP given a pair of primal and dual LPs minimize c T x subject to Ax + s = b s maximize- b T z subject to A T z + c = 0 z , classify problem as solvable, primal infeasible, or dual infeasible if solvable, find optimal x , s , z Ax + s = b, A T z + c = 0 , c T x + b T z = 0 , s , z if primal infeasible, find certificate z : A T z = 0 , z , b T z < if dual infeasible, find certificate x : Ax , c T x < Self-dual formulations 152 Methods for initialization and infeasibility detection phase I phase II minimize t subject to Ax b + t 1 , t disadvantage: phase I is as expensive as phase II big M method minimize c T x + Mt subject to Ax b + t 1 , t for some large M disadvantage: large M causes numerical problems infeasible-start methods (lecture 14) disadvantage: do not return certificate of (primal or dual) infeasibility self-dual embeddings: this lecture Self-dual formulations 153 Self-dual LP primal LP (variables u , v ) minimize f T u + g T v subject to Cu + Dv f- D T u + Ev = g u with C =- C T , E =- E T dual LP (variables u , v ) maximize- f T u- g T v subject to C u + D v f- D T u + E v = g u primal LP = dual LP we assume the problem is feasible: hence p = d =- p = 0 Self-dual formulations 154 Optimality conditions for self-dual LP...
View Full Document

This note was uploaded on 09/26/2009 for the course CAAM 236 taught by Professor Dr.vandenber during the Spring '07 term at Monmouth IL.

Page1 / 7

hsd - EE236A (Fall 2007-08) Lecture 15 Self-dual...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online