On the truncated-Newton approach for the hydropower generation management.
On diagonally-preconditioning the truncated-Newton method for super-scale linearly constrained nonlinear programming.
We present an algorithm for super-scale linearly constrained nonlinear programming (LCNP) based on Newton's method. In large scale programming solving Newton's equation at each iteration can be expensive and may not be justified when far from a local solution; we briefly review the current existing methodologies, such that by classifying the problems in small-scale, super-scale and supra-scale problems we suggest the methods that, based on our own computational experience, are more suitable in each...
Sobre la amplitud de paso multivalente en programación no lineal con condiciones lineales.
En este trabajo se describe un nuevo método para la obtención de la amplitud de paso de la dirección de búsqueda en programación no-lineal con condiciones lineales. Tradicionalmente, se considera la amplitud de paso como un escalar con valor estrictamente positivo, tal que el nuevo punto también sea factible y suficientemente descendente. En su lugar, se propone en este trabajo una amplitud de paso multivariante tal que se limita, independientemente, la amplitud de cada elemento superbásico de la...
Zero or near-to-zero Lagrange multipliers in linearly constrained nonlinear programming.
We discuss in this work the using of Lagrange multipliers estimates in linearly constrained nonlinear programming algorithms and the implication of zero or near-to-zero Lagrange multipliers. Some methods for estimating the tendency of the multipliers are proposed in the context of a given algorithm.
On diagonally preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming.
We present an algorithm for supra-scale linearly constrained nonlinear programming (LNCP) based on the Limited-Storage Quasi-Newton's method. In large-scale programming solving the reduced Newton equation at each iteration can be expensive and may not be justified when far from a local solution; besides, the amount of storage required by the reduced Hessian matrix, and even the computing time for its Quasi-Newton approximation, may be prohibitive. An alternative based on the reduced Truncated-Newton...
Lagrange multipliers estimates for constrained minimization.
We discuss in this work the first-order, second-order and pseudo-second-order estimations of Lagrange multipliers in nonlinear constrained minimization. The paper also justifies estimations and strategies that are used by two nonlinear programming algorithms that are also briefly described.
Panorámica general sobre sistemas de modelización integrada en planificación de la producción en fabricación flexible.
En este trabajo se afectúa una panorámica general de la situación actual de los sistemas de modelización para el diseño, fabricación y control de la producción en fabricación flexible; se describen los elementos que son necesarios para efectuar dicha modelización, así como los resultados que deben proporcionar un conjunto de subsistemas que, al utilizarse de una forma integrada, pueden ayudar a resolver parte de los problemas que se presentan, en líneas generales, en toda planificación de la producción...
Lower bounds strategies in combinatorial nonlinear programming. A case study: Energy generators maintenance and operation scheduling.
The Generator Maintenance and Operation Scheduling problem is presented as large-scale mixed integer non-linear programming case. Several relaxations of the integrality condition on the variables are discussed. The optimal solution of the model based on these relaxations is viewed as the lower bound of the optimal solution in the original problem. A continuous constrained non-linear programming algorithm is used in the optimization of the relaxed formulation. Computational experience on a variety...
Revisión crítica de la utilización del método del gradiente conjugado y extensiones en la minimización de funciones no lineales con condiciones.
En este trabajo se efectúa una revisión de la aplicación del método del gradiente conjugado (diseñado para resolver sistemas de ecuaciones lineales) a la optimización de funciones no lineales (no cuadráticas) en el conjunto factible definido por condiciones lineales. Se describen las desventajas de su utilización; se sugiere su sustitución por algoritmos que, precisando parecida capacidad de memoria, no adolecen de sus inconvenientes. Los resultados computacionales que se acompañan avalan esta sustitución....
On nonlinear replicated networks.
In this paper we describe a new type of network flow problem that basically consists of the classical transshipment problem with the following extensions: (1) The replication of a network by producing subnetworks with identical structure, such that they are linked by so-called linking arcs; (2) The objective function terms related to the linking arcs are nondifferentiable nonlinear functions. We also describe an implementation of a linearly constrained nonlinear programming algorithm which is fast...
Métodos para la actualización de los factores de Q y R de una matriz.
Recientemente se han propuesto varios métodos para modificar los factores Q y R de una matriz una vez que se ha eliminado (o añadido) una fila o una columna. Normalmente la descripción de estos métodos se efectúa en el contexto de una determinada aplicación; quizá sea ésta la causa de su escasa difusión.
On optimizing a maximin nonlinear function subject to replicated quasi-arborescence-like constraints.
In this paper we present the motivation for using the Truncated Newton method in an algorithm that maximises a non-linear function with additional maximin-like arguments subject to a network-like linear system of constraints. The special structure of the network (so-termed replicated quasi-arborescence) allows to introduce the new concept of independent superbasic sets and, then, using second-order information about the objective function without too much computer effort and storage.
On improving a solution to the ATSP with fixed origin and precedence relationships.
Given the directed graph G = (N, A) with a node origin and a penalty matrix C, the ATSP with fixed origin and precedence relationships (hereafter, ASTP-PR) consists of finding the permutation of the nodes from the set N, such that it minimizes a matrix C based function and does not violate the precedence relationships given by the set A. In this work we present an algorithm for improving a given feasible solution to the problem, by performing a local search that uses 3- and 4-change based procedures....
On using multistage linking constraints for stochastic optimization as a decision-making aid
We present a model1ing framework for multistage planning problems under uncertainty in the objective function coefficients and right-hand-side. A multistagy scenario analysis scheme with partial recourse is used. So, the decisíon polícy can be implemented for a given set of initial time periods (so-called implementable time stage), such that the solution for the other periods lioes not need' to be anticipated and, then, it depends upon the scenario group to occur at each stage. In any ca~e the solution...
A production planning problem in FMS.
We present in this work a hierarchical approach for generating alternatives for production planning in a generic floor shop problem within the environment of Flexible Manufacturing Systems (hereafter, FMS). Briefly, the problem can be stated as follows: Given the resources of a FMS and the characteristics of the parts to be produced along a planning horizon, obtain the loading ordering of the parts in the FMS, the execution ordering of the operations and the processing route of each part (i.e. the...
Strategies for LP-based solving a general class of scheduling problems.
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...
Page 1