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Large-scale nonlinear programming algorithm using projection methods

Paweł Białoń (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

A method for solving large convex optimization problems is presented. Such problems usually contain a big linear part and only a small or medium nonlinear part. The parts are tackled using two specialized (and thus efficient) external solvers: purely nonlinear and large-scale linear with a quadratic goal function. The decomposition uses an alteration of projection methods. The construction of the method is based on the zigzagging phenomenon and yields a non-asymptotic convergence, not dependent...

Nonlinear Rescaling Method and Self-concordant Functions

Richard Andrášik (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Nonlinear rescaling is a tool for solving large-scale nonlinear programming problems. The primal-dual nonlinear rescaling method was used to solve two quadratic programming problems with quadratic constraints. Based on the performance of primal-dual nonlinear rescaling method on testing problems, the conclusions about setting up the parameters are made. Next, the connection between nonlinear rescaling methods and self-concordant functions is discussed and modified logarithmic barrier function is...

Primal interior point method for minimization of generalized minimax functions

Ladislav Lukšan, Ctirad Matonoha, Jan Vlček (2010)

Kybernetika

In this paper, we propose a primal interior-point method for large sparse generalized minimax optimization. After a short introduction, where the problem is stated, we introduce the basic equations of the Newton method applied to the KKT conditions and propose a primal interior-point method. (i. e. interior point method that uses explicitly computed approximations of Lagrange multipliers instead of their updates). Next we describe the basic algorithm and give more details concerning its implementation...

Primal interior-point method for large sparse minimax optimization

Ladislav Lukšan, Ctirad Matonoha, Jan Vlček (2009)

Kybernetika

In this paper, we propose a primal interior-point method for large sparse minimax optimization. After a short introduction, the complete algorithm is introduced and important implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus the large sparse nonconvex minimax optimization problems can be solved successfully. The results of extensive computational experiments given in this paper confirm efficiency and robustness of the proposed...

Recursive form of general limited memory variable metric methods

Ladislav Lukšan, Jan Vlček (2013)

Kybernetika

In this report we propose a new recursive matrix formulation of limited memory variable metric methods. This approach can be used for an arbitrary update from the Broyden class (and some other updates) and also for the approximation of both the Hessian matrix and its inverse. The new recursive formulation requires approximately 4 m n multiplications and additions per iteration, so it is comparable with other efficient limited memory variable metric methods. Numerical experiments concerning Algorithm...

Solving convex program via Lagrangian decomposition

Matthias Knobloch (2004)

Kybernetika

We consider general convex large-scale optimization problems in finite dimensions. Under usual assumptions concerning the structure of the constraint functions, the considered problems are suitable for decomposition approaches. Lagrangian-dual problems are formulated and solved by applying a well-known cutting-plane method of level-type. The proposed method is capable to handle infinite function values. Therefore it is no longer necessary to demand the feasible set with respect to the non-dualized...

Strategies for LP-based solving a general class of scheduling problems.

Laureano F. Escudero, Gloria Pérez Sáinz de Rozas (1990)

Trabajos de Investigación Operativa

In this work we describe some strategies that have been proved to be very efficient for solving the following type of scheduling problems: Assume a set of jobs is to be performed along a planning horizon by selecting one from several alternatives for doing so. Besides selecting the alternative for each job, the target consists of choosing the periods at which each component of the work will be done, such that a set of scheduling and technological constraints is satisfied. The problem is formulated...

Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface

Lubomír Klimeš, Pavel Popela, Tomáš Mauder, Josef Štětina, Pavel Charvát (2017)

Kybernetika

The paper is concerned with a parallel implementation of the progressive hedging algorithm (PHA) which is applicable for the solution of stochastic optimization problems. We utilized the Message Passing Interface (MPI) and the General Algebraic Modelling System (GAMS) to concurrently solve the scenario-related subproblems in parallel manner. The standalone application combining the PHA, MPI, and GAMS was programmed in C++. The created software was successfully applied to a steel production problem...

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