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Programming Solvers (programming + solver)

Distribution by Scientific Domains
Mathematics and Statistics60%
Engineering40%

Selected Abstracts

Fast implementations and rigorous models: Can both be accommodated in NMPC?

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2008
Victor M. Zavala
Abstract In less than two decades, nonlinear model predictive control has evolved from a conceptual framework to an attractive, general approach for the control of constrained nonlinear processes. These advances were realized both through better understanding of stability and robustness properties as well as improved algorithms for dynamic optimization. This study focuses on recent advances in optimization formulations and algorithms, particularly for the simultaneous collocation-based approach. Here, we contrast this approach with competing approaches for online application and discuss further advances to deal with applications of increasing size and complexity. To address these challenges, we adapt the real-time iteration concept, developed in the context of multiple shooting (Real-Time PDE-Constrained Optimization. SIAM: Philadelphia, PA, 2007; 25,52, 3,24), to a collocation-based approach with a full-space nonlinear programming solver. We show that straightforward sensitivity calculations from the Karush,Kuhn,Tucker system also lead to a real-time iteration strategy, with both direct and shifted variants. This approach is demonstrated on a large-scale polymer process, where online calculation effort is reduced by over two orders of magnitude. Copyright © 2007 John Wiley & Sons, Ltd. [source]

An efficient linear programming solver for optimal filter synthesis

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 9 2007
Jihong Ren
Abstract We consider the problem of l, optimal deconvolution arising in high data-rate communication between integrated circuits. The optimal deconvolver can be found by solving a linear program for which we use Mehrotra's interior-point approach. The critical step is solving the linear system for the normal equations in each iteration. We show that this linear system has a special block structure that can be exploited to obtain a fast solution technique whose overall computational cost depends mostly on the number of design variables, and only linearly on the number of constraints. Numerical experiments validate our findings and illustrate the merits of our approach. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Passification-based adaptive control of linear systems: Robustness issues

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2008
Dimitri Peaucelle
Abstract Passivity is a widely used concept in control theory having led to many significant results. This paper concentrates on one characteristic of passivity, namely passification-based adaptive control. This concept applies to multi-input multi-output systems for which exists a combination of outputs that renders the open-loop system hyper-minimum phase. Under such assumptions, the system may be passified by both high-gain static output feedback and by a particular adaptive control algorithm. This last control law is modified here to guarantee its coefficients to be bounded. The contribution of this paper is to investigate its robustness with respect to parametric uncertainty. Time response characteristics are illustrated on examples including realistic situations with noisy output and saturated input. Theoretical results are formulated as linear matrix inequalities and can hence be readily solved with semi-definite programming solvers. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Bicriteria product design optimization: An efficient solution procedure using AND/OR trees

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 6 2002
S. Raghavan
Competitive imperatives are causing manufacturing firms to consider multiple criteria when designing products. However, current methods to deal with multiple criteria in product design are ad hoc in nature. In this paper we present a systematic procedure to efficiently solve bicriteria product design optimization problems. We first present a modeling framework, the AND/OR tree, which permits a simplified representation of product design optimization problems. We then show how product design optimization problems on AND/OR trees can be framed as network design problems on a special graph,a directed series-parallel graph. We develop an enumerative solution algorithm for the bicriteria problem that requires as a subroutine the solution of the parametric shortest path problem. Although this parametric problem is hard on general graphs, we show that it is polynomially solvable on the series-parallel graph. As a result we develop an efficient solution algorithm for the product design optimization problem that does not require the use of complex and expensive linear/integer programming solvers. As a byproduct of the solution algorithm, sensitivity analysis for product design optimization is also efficiently performed under this framework. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 574,592, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10031 [source]

A column generation approach for SONET ring assignment

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2006
Elder M. Macambira
Abstract In this article we consider the SONET ring assignment problem (SRAP) presented in 7. The authors pointed out the inadequacy of solving SRAP instances using their integer programming formulation and commercial linear programming solvers. Similar experiences with IP models for SRAP are reported in 1. In this article we reformulate SRAP as a set partitioning model with an additional knapsack constraint. This new formulation has an exponential number of columns and, to solve it, we implemented a branch-and-price/column generation algorithm. Extensive computational experiments showed that the new algorithm is orders of magnitude faster than standard branch-and-bound codes running on compact IP models introduced earlier. Instances taken from 1, 7, which could not be solved there in hours of computation were solved here to optimality in just a few seconds. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 47(3), 157,171 2006 [source]