This paper develops a methodology for decision-making in organizationally distributed systems where decision authorities and information are dispersed in multiple organizations. Global performance is achieved through ...
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This paper develops a methodology for decision-making in organizationally distributed systems where decision authorities and information are dispersed in multiple organizations. Global performance is achieved through cooperative interaction and partial information sharing among organizations. The information shared among organizations is contrived using modified Lagrangian relaxation techniques. Novel to the methodology is that no single master problem with a global view of the system is required to guide the decision process. Rather, multiple artificial decision entities, termed Coupling Agents, are associated with subsets of coupling constraints. The proposed generic model can be applied to decision-making problems with a variety of mathematical structures. In this paper the methodology is applied to parameter design problems to illustrate the behavior of the proposed methodology in the realm of non-linear optimization.
Algorithms for estimating temperatures at arbitrary nodes of steady-state thermal network models, given noisy measured values of a subset of the nodes of the network, are described. Applications where temperature esti...
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Algorithms for estimating temperatures at arbitrary nodes of steady-state thermal network models, given noisy measured values of a subset of the nodes of the network, are described. Applications where temperature estimation is desired include correlation of test and analysis results, thermal-stress estimation, and others. An optimization problem is formulated to recover the temperatures at the unobservable nodes. This problem is an example of nonlinear, least-squares minimization with a single quadratic constraint (imposed by the measured data) and is solved with the method of Lagrange multipliers. New algorithms are developed that find local minima of the cost functional through a Newton-type iteration procedure. At each iteration a least-squares problem with a quadratic inequality is solved with a fast and memory-efficient method. The proposed algorithms are shown to be at least an order of magnitude faster than standard algorithms. Their accuracy and speed are examined through a series of tests on thermal models from ongoing NASA missions.
Using standard nonlinear programming (NLP) theory, we establish formulas for first and second order directional derivatives of optimal value functions of parametric mathematical programs with complementarity constrain...
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Using standard nonlinear programming (NLP) theory, we establish formulas for first and second order directional derivatives of optimal value functions of parametric mathematical programs with complementarity constraints (MPCCs). The main point is that under a linear independence condition on the active constraint gradients, optimal value sensitivity of MPCCs is essentially the same as for nonlinear programs, in spite of the combinatorial nature of the MPCC feasible set. Unlike NLP however, second order directional derivatives of the MPCC optimal value function show combinatorial structure.
The design problem of a shaded-pole induction motor is represented as a vector optimization problem. The problem is solved using a nonlinear programming technique. The motor is designed with different requirements. Th...
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The design problem of a shaded-pole induction motor is represented as a vector optimization problem. The problem is solved using a nonlinear programming technique. The motor is designed with different requirements. These requirements are represented by weighted elements of objective function vector and a set of constraints. The objective functions are the goals of design procedure where the designer tries to achieve their extreme (optimal) values. The adopted approach provides the flexibility for the designer to represent the importance of goals in "weights" and find the optimal design according to these weights. Implementation of this approach is presented by designing a motor with two objective functions (starting torque and cost). The results obtained verify the ability of this approach to achieve valuable improvements.
It is known that the optimal control may introduce significant economical benefits into production processes, thus being an important and challenging research area with practical relevance. The modeling and optimizati...
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It is known that the optimal control may introduce significant economical benefits into production processes, thus being an important and challenging research area with practical relevance. The modeling and optimization of biotechnological processes has been object of research and their related results have generated improvements in operating conditions and strategies, however, the inherent features of dynamical bioprocesses prevent the application of conventional optimization algorithms, hence making necessary the development of tailored methods and strategies. The objective of this work is to develop mathematical programming strategies for simultaneous optimization of dynamic systems and evaluate their computational performance. Simultaneous optimization with orthogonal collocation is applied to a simplified model for biosynthesis of penicillin from glucose, which was studied by Cuthrell and Biegler (1989). The results show that discretization of differential equations systems (DAE) by orthogonal collocation in finite elements efficiently transforms dynamic optimization problems into nonlinear programming (NLP) problems, enabling to solve complex problems with several control variables and minimizing the approximation error.
Interior methods are an omnipresent, conspicuous feature of the constrained optimization landscape today, but it was not always so. Primarily in the form of barrier methods, interior-point techniques were popular duri...
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Interior methods are an omnipresent, conspicuous feature of the constrained optimization landscape today, but it was not always so. Primarily in the form of barrier methods, interior-point techniques were popular during the 1960s for solving nonlinearly constrained problems. However, their use for linear programming was not even contemplated because of the total dominance of the simplex method. Vague but continuing anxiety about barrier methods eventually led to their abandonment in favor of newly emerging, apparently more efficient alternatives such as augmented Lagrangian and sequential quadratic programming methods. By the early 1980s, barrier methods were almost without exception regarded as a closed chapter in the history of optimization. This picture changed dramatically with Karmarkar's widely publicized announcement in 1984 of a fast polynomial-time interior method for linear programming;in 1985, a formal connection was established between his method and classical barrier methods. Since then, interior methods have advanced so far, so fast, that their influence has transformed both the theory and practice of constrained optimization. This article provides a condensed, selective look at classical material and recent research about interior methods for nonlinearly constrained optimization.
To improve the previously developed dual-type (DT) method used in solving optimal power flow (OPF) problems with large number of thermal-limit constraints, we propose two new techniques in this paper. The first one is...
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To improve the previously developed dual-type (DT) method used in solving optimal power flow (OPF) problems with large number of thermal-limit constraints, we propose two new techniques in this paper. The first one is a graph-method based decomposition technique which can decompose the large-dimension projection problem, caused by the large number of thermal-limit constraints, into several independent medium-dimension projection subproblems at the expense of slight increment of the dual problem's dimension. The second technique is an active-set strategy based DT method which can solve the medium-dimension projection subproblems efficiently. We have used the DT method embedded with these two new techniques in solving numerous OPF's with large number of thermal-limit constraints. The test results show that the proposed techniques are very efficient and effectively improve the DT method for handling large number of thermal-limit constraints.
The paper considers a sequential Design Of Experiments (DOE) scheme. Our objective is to maximize both information and economic measures over a feasible set of experiments. Optimal DOE strategies are developed by intr...
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The paper considers a sequential Design Of Experiments (DOE) scheme. Our objective is to maximize both information and economic measures over a feasible set of experiments. Optimal DOE strategies are developed by introducing information criteria based on measures adopted from information theory. The evolution of acquired information along various stages of experimentation is analyzed for linear models with a Gaussian noise term. We show that for particular cases, although the amount of information is unbounded, the desired rate of acquiring information decreases with the number of experiments. This observation implies that at a certain point in time it is no longer efficient to continue experimenting. Accordingly, we investigate methods of stochastic dynamic programming under imperfect state information as appropriate means to obtain optimal experimentation policies. We propose cost-to-go functions that model the trade-off between the cost of additional experiments and the benefit of incremental information. We formulate a general stochastic dynamic programming framework for design of experiments and illustrate it by analytic and numerical implementation examples.
An affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods is presented. The theory is used for the construction of an accuracy matching between iteration errors and truncation errors, which...
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An affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods is presented. The theory is used for the construction of an accuracy matching between iteration errors and truncation errors, which arise from the inexact linear system solvers. The theoretical investigations are illustrated numerically by an optimal control problem for the Burgers equation.
A maximum likelihood approach has been proposed for finding protein binding sites on strands of DNA [G.D. Stormo, G.W. Hartzell, Proceedings of the National Academy of Sciences of the USA 86 (1989) 1183]. We formulate...
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A maximum likelihood approach has been proposed for finding protein binding sites on strands of DNA [G.D. Stormo, G.W. Hartzell, Proceedings of the National Academy of Sciences of the USA 86 (1989) 1183]. We formulate an optimization model for the problem and present calculations with experimental sequence data to study the behavior of this site identification method. (C) 2002 Elsevier Science B.V. All rights reserved.
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