An Interior-Point Krylov-Orthogonal Projection Method for Nonlinear Programming
In this work we consider an inexact Newton's method implementation of the primal-dual interior-point algorithm for solving general nonlinear programming problems recently introduced by Argáez and Tapia. This inexact method is designed to solve large scale problems. The iterative solution technique uses an orthogonal projection - Krylov subspace scheme to solve the highly indefinite and nonsymmetric linear systems associated with nonlinear programming. Our iterative method is a projection method that maintains linearized feasibility with respect to both the equality constraints and the complementarity conditions. This guarantees that in each iteration the linear solver generates a descent direction, so that the iterative solver is not required to find a Newton step but rather cheaply provides a way to march toward an optimal solution of the problem. This makes the use of a preconditioner inconsequential except near the solution of the problem, where the Newton step is effective. Moreover, we limit the problem to finding a good preconditioner only for the Hessian of the Lagrangian function associated with the problem plus a positive diagonal matrix. We report numerical experimentation for several large scale problems to illustrate the viability of the method.
Citable link to this pagehttps://hdl.handle.net/1911/101893
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