In this paper, we survey the most recent methods that have been developed for the solution of semidefinite programs. We first concentrate on the methods that have been primarily motivated by the interior point (IP) algorithms for linear programming, putting special emphasis in the class of primal-dual path-following algorithms. We also survey methods that have … Read more
For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form “minimize an augmented Lagrangian function subject to linearized constraints”. Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. The well known software package MINOS has proven effective on many … Read more
A framework for proving global convergence for a class of line search filter type methods for nonlinear programming is presented. The underlying method is based on the dominance concept of multiobjective optimization where trial points are accepted provided there is a sufficient decrease in the objective function or constraints violation function. The proposed methods solve … Read more
In this paper, we propose an algorithm for solving nonlinear nonconvex programming problems, which is based on the nonsmooth equation approach. This Algorithm was implemented in the interactive system for universal functional optimization UFO. Results of numerical experiments are reported. Citation Report V844, Institute of Computer Science, AV CR, Pod Vodarenskou Vezi 2, 18207 Praha … Read more
In this paper, we propose an algorithm for solving nonlinear nonconvex programming problems, which is based on the interior-point approach. Main theoretical results concern direction determination and step-length selection. We split inequality constraints into active and inactive to overcome problems with stability. Inactive constraints are eliminated directly while active constraints are used to define symmetric … Read more
This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained … Read more
We propose and analyze a primal-dual interior point method of the “feasible” type, with the additional property that the objective function decreases at each iteration. A distinctive feature of the method is the use of different barrier parameter values for each constraint, with the purpose of better steering the constructed sequence away from non-KKT stationary … Read more
Transition to superlinear local convergence is shown for a modified version of the trust-region filter-SQP method for nonlinear programming introduced by Fletcher, Leyffer, and Toint [8]. Hereby, the original trust-region SQP-steps can be used without an additional second order correction. The main modification consists in using the Lagrangian function value instead of the objective function … Read more
This paper describes numerical experience with solving MPECs as NLPs on a large collection of test problems. The key idea is to use off-the-shelf NLP solvers to tackle large instances of MPECs. It is shown that SQP methods are very well suited to solving MPECs and at present outperform Interior Point solvers both in terms … Read more
An algorithm for smooth nonlinear constrained optimization problems is described, in which a sequence of feasible iterates is generated by solving a trust-region sequential quadratic programming (SQP) subproblem at each iteration, and perturbing the resulting step to retain feasibility of each iterate. By retaining feasibility, the algorithm avoids several complications of other trust-region SQP approaches: … Read more