Dual versus primal-dual interior-point methods for linear and conic programming

Dual versus primal-dual interior-point methods for linear and conic programming

We observe a curious property of dual versus primal-dual path-following interior-point methods when applied to unbounded linear or conic programming problems in dual form. While primal-dual methods can be viewed as implicitly following a central path to detect primal infeasibility and dual unboundedness, dual methods can sometimes implicitly move away from the analytic center of the set of infe...

Primal-dual interior-point methods

3. page 13, lines 12–13: Insert a phrase to stress that we consider only monotone LCP in this book, though the qualifier ”monotone” is often omitted. Replace the sentence preceding the formula (1.21) by The monotone LCP—the qualifier ”monotone” is implicit throughout this book—is the problem of finding vectors x and s in I R that satisfy the following conditions: 4. page 13, line −12: delete “o...

Target Directions for Primal-dual Interior-point Methods for Self-scaled Conic Programming

The theory of self-scaled conic programming provides a uniied framework for the theories of linear programming, semideenite programming and convex quadratic programming with convex quadratic constraints. In the linear programming literature there exists a unifying framework for the analysis of various important classes of interior-point algorithms, known under the name of target-following algor...

A Primal-Dual Interior Point Algorithm for Linear Programming

This chapter presents an algorithm that works simultaneously on primal and dual linear programming problems and generates a sequence of pairs of their interior feasible solutions. Along the sequence generated, the duality gap converges to zero at least linearly with a global convergence ratio (1 Yf/n); each iteration reduces the duality gap by at least Yf/n. Here n denotes the size of the probl...

Semidefinite Programming : Formulations and Primal - Dual Interior - Point Methods