This paper is an introduction to Newton, a constrain-programming language over nonlinear real constraints. Newton originates from an effort to reconcile the declarative nature of constraint logic programming (CLP) lan...
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This paper is an introduction to Newton, a constrain-programming language over nonlinear real constraints. Newton originates from an effort to reconcile the declarative nature of constraint logic programming (CLP) languages over intervals with advanced interval techniques developed in numerical analysis, such as the interval Newton method. Its key conceptual idea is to introduce the notion of box-consistency, which approximates are-consistency, a notion well-known in artificial intelligence. Box-consistency achieves an effective pruning at a reasonable computation cost and generalizes some traditional interval operators. Newton has been applied to numerous applications in science and engineering, including nonlinear equation-solving, unconstrained optimization, and constrained optimization. It is competitive with continuation methods on their equation-solving benchmarks and outperforms the interval-based methods we are aware of on optimization problems. (C) 1998 Elsevier Science B.V.
This paper is an introduction to Newton, a constraint programming language over nonlinear real constraints. Newton originates from an effort to reconcile the declarative nature of constraint logic programming (CLP) la...
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This paper is an introduction to Newton, a constraint programming language over nonlinear real constraints. Newton originates from an effort to reconcile the declarative nature of constraint logic programming (CLP) languages over intervals with advanced interval techniques developed in numerical analysis, such as the interval Newton method. Its key conceptual idea is to introduce the notion of box-consistency, which approximates arc-consistency, a notion well-known in artificial intelligence. Box-consistency achieves an effective pruning at a reasonable computation cost and generalizes some traditional interval operators. Newton has been applied to numerous applications in science and engineering, including nonlinear equation-solving, unconstrained optimization, and constrained optimization. It is competitive with continuation methods on their equation-solving benchmarks and outperforms the interval-based methods we are aware of on optimization problems.
To remain competitive firms need to develop long-term strategies for acquiring and using advanced engineering and manufacturing technologies. However, there are innumerable alternatives for obtaining internally and/or...
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To remain competitive firms need to develop long-term strategies for acquiring and using advanced engineering and manufacturing technologies. However, there are innumerable alternatives for obtaining internally and/or externally the personnel and equipment resources needed to employ advanced technologies. A mixed integer, nonlinear programing model (MINP/L) is presented which identifies the optimal alternative for long-term capacity and acquisition planning for advanced technology resource requirements while allowing the personnel and equipment to have realistic nonlinear performance improvement (learning) or decay capabilities. A example problem is provided and an optimal solution is obtained and compared to the results of more common, but also more expensive, solutions. Numerous future research extensions are offered.
Mathematical functions describe virtual 'n' dimensional worlds exhibiting the most strange topology one can imagine. To find optimum points means to climb the highest mountains of these fantasy realms, taking ...
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Mathematical functions describe virtual 'n' dimensional worlds exhibiting the most strange topology one can imagine. To find optimum points means to climb the highest mountains of these fantasy realms, taking care by not being deceived by false maximums. Usually, inside these kingdoms, there are forbidden zones places that must be avoided. Most of the times one become lost inside these prohibited territories, even without noting it. The search for good and fast algorithms to guide the traveler in his journey toward the pot of gold hidden in these heights tells a never ending story where, everyday, a new record is established. Like in a Olympic game, the yesterday impossible is inevitably beaten by some ignominious ignorant that doesn't know that such a record could not be overthrown. This paper tells the story of this search and suggests some approaches to enhance the performance of nowadays optimization algorithms.
General conditions are presented for the convergence of methods for solving conditional minimization problems. The conditions are necessary and sufficient for a certain class of sequential methods for unconditional mi...
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General conditions are presented for the convergence of methods for solving conditional minimization problems. The conditions are necessary and sufficient for a certain class of sequential methods for unconditional minimization. They are further generalized to problems of multicriterial optimization. The conditions have a clear geometric interpretation.
We present modifications of the generalized conjugate gradient algorithm of Liu and Storey for unconstrained optimization problems (Ref. 1), extending its applicability to situations where the search directions are no...
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We present modifications of the generalized conjugate gradient algorithm of Liu and Storey for unconstrained optimization problems (Ref. 1), extending its applicability to situations where the search directions are not defined. The use of new search directions is proposed and one additional condition is imposed on the inexact line search. The convergence of the resulting algorithm can be established under standard conditions for a twice continuously differentiable function with a bounded level set. Algorithms based on these modifications have been tested on a number of problems, showing considerable improvements. Comparisons with the BFGS and other quasi-Newton methods are also given.
A new formulation is presented for the analysis of multireservoir systems, based on the development of first and second moment expressions for the stochastic storage state variables. These expressions give explicit co...
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A new formulation is presented for the analysis of multireservoir systems, based on the development of first and second moment expressions for the stochastic storage state variables. These expressions give explicit consideration to the maximum and minimum storage bounds in the reservoir system, a feature not incorporated in some existing formulations based on traditional control theory. Using this analysis, expected values of the storage states, variances of storage, release policies, reliability levels, and failure probabilities (useful information in the context of reservoir operations and design) can be obtained from a nonlinear programming solution. The approach does not involve any discretization of the system variables. The results for the means and standard deviations of the storage states for a multireservoir system compare favorably with those obtained from simulation.
In this paper we consider a loss system where the arrivals can be classified into different groups according to their arrival rate and expected service time. While the standard admission policy consists of rejecting o...
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In this paper we consider a loss system where the arrivals can be classified into different groups according to their arrival rate and expected service time. While the standard admission policy consists of rejecting only those customers who arrive when all servers are busy, we address the problem of finding the optimal static admission policy (with respect to a given reward structure) when customers can be discriminated according to the group they belong to, thus customers of some groups might be automatically rejected (even if some servers remain idle) in order to enhance the global efficiency of the system. The optimality of a c mu-rule is shown, from which finite-time algorithms for the one-and two-server cases are derived.
We consider an optimization formulation that captures the quality of a grasp. In this model the object geometry, finger contact points and the magnitude of the external Load are given. Perturbation of these parameters...
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We consider an optimization formulation that captures the quality of a grasp. In this model the object geometry, finger contact points and the magnitude of the external Load are given. Perturbation of these parameters from their nominal values might lead to significant variations on the predicted grasping quality measures. In this paper we study the sensitivity of a class of grasping quality functions subject to these perturbations and introduce a global sensitivity measure together with a computational procedure to evaluate it. Our analysis is developed within the framework of sensitivity theory and dual methods of nonlinear programming. Numerical simulations supporting the theoretical analysis are presented.
Successful treatment of inconsistent QP problems is of major importance in the SQP method, since such occur quite often even for well behaved nonlinear programming problems. This paper presents a new technique for reg...
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Successful treatment of inconsistent QP problems is of major importance in the SQP method, since such occur quite often even for well behaved nonlinear programming problems. This paper presents a new technique for regularizing inconsistent QP problems, which compromises in its properties between the simple technique of Pantoja and Mayne [36] and the highly successful, but expensive one of Tone [47]. Global convergence of a corresponding algorithm is shown under reasonable weak conditions. Numerical results are reported which show that this technique, combined with a special method for the case of regular subproblems, is quite competitive to highly appreciated established ones.
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