241,823 research outputs found

    A merit function approach for direct search

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    In this paper it is proposed to equip direct-search methods with a general procedure to minimize an objective function, possibly nonsmooth, without using derivatives and subject to constraints on the variables. One aims at considering constraints, most likely nonlinear or nonsmooth, for which the derivatives of the corresponding functions are also unavailable. The novelty of this contribution relies mostly on how relaxable constraints are handled. Such constraints, which can be relaxed during the course of the optimization, are taken care of by a merit function and, if necessary, by a restoration procedure. Constraints that are unrelaxable, when present, are treated by an extreme barrier approach. One is able to show that the resulting merit function direct-search algorithm exhibits global convergence properties for first-order stationary constraints. As in the progressive barrier method [C. Audet and J. E. Dennis Jr., SIAM J. Optim., 20 (2009), pp. 445--472], we provide a mechanism to indicate the transfer of constraints from the relaxable set to the unrelaxable one

    A Merit Function Approach for Direct Search

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    A Simple and Efficient Algorithm for Nonlinear Model Predictive Control

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    We present PANOC, a new algorithm for solving optimal control problems arising in nonlinear model predictive control (NMPC). A usual approach to this type of problems is sequential quadratic programming (SQP), which requires the solution of a quadratic program at every iteration and, consequently, inner iterative procedures. As a result, when the problem is ill-conditioned or the prediction horizon is large, each outer iteration becomes computationally very expensive. We propose a line-search algorithm that combines forward-backward iterations (FB) and Newton-type steps over the recently introduced forward-backward envelope (FBE), a continuous, real-valued, exact merit function for the original problem. The curvature information of Newton-type methods enables asymptotic superlinear rates under mild assumptions at the limit point, and the proposed algorithm is based on very simple operations: access to first-order information of the cost and dynamics and low-cost direct linear algebra. No inner iterative procedure nor Hessian evaluation is required, making our approach computationally simpler than SQP methods. The low-memory requirements and simple implementation make our method particularly suited for embedded NMPC applications

    Estimating variances and covariances for multivariate animal models by restricted maximum likelihood

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    Restricted Maximum Likelihood estimates of variance and covariance components can be obtained by direct maximization of the associated likelihood using standard, derivative-free optimization procedures. In general, this requires a multi-dimensional search and numerous evaluations of the (log) likelihood function. Use of this approach for analyses under an Animal Model has been described for the univariate case. This model includes animals' additive genetic merit as random e#ect and accounts for all relationships between animals. In addition, other random factors such as common environmental or maternal genetic e#ects can be fitted. This paper describes the extension to multivariate analyses, allowing for missing records. A numerical example is given and simplifications for specific models are discussed. Keywords : Variance components, Restricted Maximum Likelihood, Animal Model, additional random e#ects, derivative-free approach, multivariate analysis 1. Introduction In the statistic..

    Hybrid Newton-type method for a class of semismooth equations

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    In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite-difference Newton method to an inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear or quadratic. We report also several numerical results obtained applying the method to suitable reformulations of well-known nonlinear complementarity problem

    Comparative study on the application of evolutionary optimization techniques to orbit transfer maneuvers

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    Orbit transfer maneuvers are here considered as benchmark cases for comparing performance of different optimization techniques in the framework of direct methods. Two different classes of evolutionary algorithms, a conventional genetic algorithm and an estimation of distribution method, are compared in terms of performance indices statistically evaluated over a prescribed number of runs. At the same time, two different types of problem representations are considered, a first one based on orbit propagation and a second one based on the solution of Lambert’s problem for direct transfers. In this way it is possible to highlight how problem representation affects the capabilities of the considered numerical approaches

    Algebraic and algorithmic frameworks for optimized quantum measurements

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    Von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are however static processes that do not adapt to the states they measure. Advances in the field of adaptive measurement have shown that this limitation can be overcome by "wrapping" the von Neumann projectors in a higher-dimensional circuit which exploits the interplay between measurement outcomes and measurement settings. Unfortunately, the design of adaptive measurement has often been ad hoc and setup-specific. We shall here develop a unified framework for designing optimized measurements. Our approach is two-fold: The first is algebraic and formulates the problem of measurement as a simple matrix diagonalization problem. The second is algorithmic and models the optimal interaction between measurement outcomes and measurement settings as a cascaded network of conditional probabilities. Finally, we demonstrate that several figures of merit, such as Bell factors, can be improved by optimized measurements. This leads us to the promising observation that measurement detectors which---taken individually---have a low quantum efficiency can be be arranged into circuits where, collectively, the limitations of inefficiency are compensated for
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