Optimization methods that employ the classical Powell-Hestenes-Rockafellar Augmented Lagrangian are useful tools for solving Nonlinear Programming problems. Their reputation decreased in the last ten years due to the comparative success of Interior-Point Newtonian algorithms, which are asymptotically faster. In the present research a combination of both approaches is evaluated. The idea is to p...

Quadratic programs obtained for optimal control problems of dynamic or discrete-time processes usually involve highly block structured Hessian and constraints matrices, to be exploited by efficient numerical methods. In interior point methods, this is elegantly achieved by the widespread availability of advanced sparse symmetric indefinite factorization codes. For active set methods, however, c...

An infeasible interior-point algorithm for solving the$P_*$-matrix linear complementarity problem based on a kernelfunction with trigonometric barrier term is analyzed. Each (main)iteration of the algorithm consists of a feasibility step andseveral centrality steps, whose feasibility step is induced by atrigonometric kernel function. The complexity result coincides withthe best result for infea...

named interior points set of the LCP (M, q) must be nonempty. The aim of this paper is to show that the LCP (M, q) is completely equivalent to a convex quadratic programming problem (CQPP ) under linear constraints. To solve the second problem, we propose an iterative method of interior points which converge in polynomial time to the exact solution; this convergence requires at most o(n0,5L) it...

We propose a new infeasible path-following algorithm for convex linearlyconstrained quadratic programming problem. This algorithm utilizes the monomial method rather than Newton's method for solving the KKT equations at each iteration. As a result, the sequence of iterates generated by this new algorithm is infeasible in the primal and dual linear constraints, but, unlike the sequence of iterat...

In this paper we briefly review the importance of LP (linear programming), and Dantzig’s main contributions to OR (Operations Research), mathematics, and computer science. In [11, 3] gravitational methods for LP have been introduced. Several versions exist. The three main versions discussed there use a ball of (a): 0 radius, (b): small positive radius, and (c): the ball of largest possible radi...

In this paper, we introduce the truncated primal-infeasible dual-feasible interior point algorithm for linear programming and describe an implementation of this algorithm for solving the minimum cost network flow problem. In each iteration, the linear system that determines the search direction is computed inexactly, and the norm of the resulting residual vector is used in the stopping criteria...

We show that an interior-point method for monotone variational inequalities exhibits superlinear convergence provided that all the standard assumptions hold except for the well-known assumption that the Jacobian of the active constraints has full rank at the solution. We show that superlinear convergence occurs even when the constant-rank condition on the Jacobian assumed in an earlier work doe...

(Rece;"cd 00 Monlh 20Ox; final ...,rsiaH recei"ed 00 Monlh £OOX) In this paper a primal-dual interior-point algorithm for semidefinite programming that can be used for analrzing e.g_ polytopic linear difleTential indusions is tailored in order to be more computationally efficient. The key to th" speedup is to allow for inexact ..,,,rch directions in the inteciOT_point algorithm. Th.,..., are ob...

In this paper we propose a new large-update primal-dual interior point algorithm for P∗( ) linear complementarity problems (LCPs). We generalize Bai et al.’s [A primal-dual interior-point method for linear optimization based on a new proximity function, Optim. Methods Software 17(2002) 985–1008] primal-dual interior point algorithm for linear optimization (LO) problem to P∗( ) LCPs. New search ...