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 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
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. CitationReport V844, Institute of Computer Science, AV CR, Pod Vodarenskou Vezi 2, 18207 Praha 8, … Read more
At the Fraunhofer Institute UMSICHT a nonlinear model has been developed facilitating the dynamic optimisation of combined heat and power production systems. The strategy called “dynamic supply temperature optimisation” is a very promising approach to use the DH-network itself as a large heat storage causing no additional investment cost. The pipeline system of a district … 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
This paper concerns general (nonconvex) nonlinear optimization when first and second derivatives of the objective and constraint functions are available. The proposed method is based on finding an approximate solution of a sequence of unconstrained subproblems parameterized by a scalar parameter. The objective function of each unconstrained subproblem is an augmented penalty-barrier function that involves … 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
We propose the elastic string algorithm for computing mountain passes in finite-dimensional problems. We analyze the convergence properties and numerical performance of this algorithm for benchmark problems in chemistry and discretizations of infinite-dimensional variational problems. We show that any limit point of the elastic string algorithm is a path that crosses a critical point at … Read more