We present a sequential quadratic optimization (SQO) algorithm for nonlinear constrained optimization. The method attains all of the strong global and fast local convergence guarantees of classical SQO methods, but has the important additional feature that fast local convergence is guaranteed when the algorithm is employed to solve infeasible instances. A two-phase strategy, carefully constructed … Read more
We present local convergence analysis of the method of multipliers for equality-constrained variational problems (in the special case of optimization, also called the augmented Lagrangian method) under the sole assumption that the dual starting point is close to a noncritical Lagrange multiplier (which is weaker than second-order sufficiency). Local superlinear convergence is established under the … Read more
The structure of many real-world optimization problems includes minimization of a nonlinear (or quadratic) functional subject to bound and singly linear constraints (in the form of either equality or bilateral inequality) which are commonly called as continuous knapsack problems. Since there are efficient methods to solve large-scale bound constrained nonlinear programs, it is desirable to … Read more
In this chapter we present a primal-dual interior point algorithm for solving constrained nonlinear programming problems. Switching rules are implemented that aim at exploiting the merits and avoiding the drawbacks of three different merit functions. The penalty parameter is determined using an adaptive penalty strategy that ensures a descent property for the merit function. The … Read more
A new class of infeasible interior point methods for solving sufficient linear complementarity problems requiring one matrix factorization and $m$ backsolves at each iteration is proposed and analyzed. The algorithms from this class use a large $(\caln_\infty^-$) neighborhood of an infeasible central path associated with the complementarity problem and an initial positive, but not necessarily … Read more
A first order affine scaling method and two $m$th order affine scaling methods for solving monotone linear complementarity problems (LCP) are presented. All three methods produce iterates in a wide neighborhood of the central path. The first order method has $O(nL^2(\log nL^2)(\log\log nL^2))$ iteration complexity. If the LCP admits a strict complementary solution then both … Read more
We correct an error in Algorithm 2 from the paper with the same name that was published in Mathematical Programming, Ser. A, 100, 2(2004), 317–337. Citationsubmitted to Mathematical ProgrammingArticleDownload View PDF
We correct an error in Algorithms 4.1 and 4.8 from the paper with the same title that was published in Optimization Methods and Software, 20, 1 (2005), 145–168. Citationsubmitted to Optimization Methods and SoftwareArticleDownload View PDF
Two corrector-predictor interior point algorithms are proposed for solving mono\-tone linear complementarity problems. The algorithms produce a sequence of iterates in the $\caln_{\infty}^{-}$ neighborhood of the central path. The first algorithm uses line search schemes requiring the solution of higher order polynomial equations in one variable, while the line search procedures of the second algorithm … Read more
In \cite{SPT} the authors considered a variant of Mehrotra’s predictor-corrector algorithm that has been widely used in several IPMs based optimization packages. By an example they showed that this variant might make very small steps in order to keep the iterate in a certain neighborhood of the central path, that itself implies the inefficiency of … Read more