We propose a new class of incremental primal-dual techniques for solving nonlinear programming problems with special structure. Specifically, the objective functions of the problems are sums of independent nonconvex c...
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We propose a new class of incremental primal-dual techniques for solving nonlinear programming problems with special structure. Specifically, the objective functions of the problems are sums of independent nonconvex continuously differentiable terms minimized subject to a set of nonlinear constraints for each term. The technique performs successive primal-dual increments for each decomposition term of the objective function. The primal-dual increments are calculated by performing one Newton step towards the solution of the Karush-Kuhn-Tucker optimality conditions of each subproblem associated with each objective function term. We show that the resulting incremental algorithm is q-linearly convergent under mild assumptions for the original problem.
In this paper we consider inequality constrained nonlinear optimization problems where the first order derivatives of the objective function and the constraints cannot be used. Our starting point is the possibility to...
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In this paper we consider inequality constrained nonlinear optimization problems where the first order derivatives of the objective function and the constraints cannot be used. Our starting point is the possibility to transform the original constrained problem into an unconstrained or linearly constrained minimization of a nonsmooth exact penalty function. This approach shows two main difficulties: the first one is the nonsmoothness of this class of exact penalty functions which may cause derivative-free codes to converge to nonstationary points of the problem;the second one is the fact that the equivalence between stationary points of the constrained problem and those of the exact penalty function can only be stated when the penalty parameter is smaller than a threshold value which is not known a priori. In this paper we propose a derivative-free algorithm which overcomes the preceding difficulties and produces a sequence of points that admits a subsequence converging to a Karush-Kuhn-Tucker point of the constrained problem. In particular the proposed algorithm is based on a smoothing of the nondifferentiable exact penalty function and includes an updating rule which, after at most a finite number of updates, is able to determine a "right value" for the penalty parameter. Furthermore we present the results obtained on a real world problem concerning the estimation of parameters in an insulin-glucose model of the human body.
A novel idea is proposed for solving optimization problems with equality constraints and bounds on the variables. In the spirit of sequential quadratic programming and sequential linearly-constrained programming, the ...
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A novel idea is proposed for solving optimization problems with equality constraints and bounds on the variables. In the spirit of sequential quadratic programming and sequential linearly-constrained programming, the new proposed approach approximately solves, at each iteration, an equality-constrained optimization problem. The bound constraints are handled in outer iterations by means of an augmented Lagrangian scheme. Global convergence of the method follows from well-established nonlinear programming theories. Numerical experiments are presented.
In this paper, we explore the verification problem of outsourcing constrained nonlinear programming (NLP) when it is required to be solved by particle swarm optimization (PSO) algorithm, i.e., making sure that the clo...
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In this paper, we explore the verification problem of outsourcing constrained nonlinear programming (NLP) when it is required to be solved by particle swarm optimization (PSO) algorithm, i.e., making sure that the cloud runs PSO algorithm faithfully and returns an acceptable solution. An efficient verification scheme without any cryptographic tool is proposed. The proposed scheme involves approximate KKT conditions with the epsilon-KKT point in verifying the optimality of the result returned by PSO algorithm. Extensive experiments on PSO benchmarks and NLP test problems demonstrate that our proposed scheme is effective and efficient at verifying the cloud's honesty.
In this work, Huard type converse duality theorems for scalar and multiobjective second-order dual problems in nonlinear programming are established. (C) 2007 Elsevier Ltd. All rights reserved.
In this work, Huard type converse duality theorems for scalar and multiobjective second-order dual problems in nonlinear programming are established. (C) 2007 Elsevier Ltd. All rights reserved.
One of the greatest challenges in the electricity generation sector is to operate hydrothermal plants in view of the randomness of hydrological events and climate change, that may impact the inflows into the systems. ...
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One of the greatest challenges in the electricity generation sector is to operate hydrothermal plants in view of the randomness of hydrological events and climate change, that may impact the inflows into the systems. In several Brazilian watersheds, conflicts among water users are already registered, in addition to inflow changes that affect the electricity generation system. The Sao Francisco River Basin (SFRB) is an important source of water for the development of northeastern Brazil. In this context, this work aimed at carrying out a study on the statistical behavior of time series related to the management of the SFRB hydrosystem network, as well as to measure the performance of hydropower plants in supplying multiple users, in different critical periods. Historical records of natural streamflow, natural inflow energy and stored energy were used. Some statisctical tests were applied to detect trends and change-points. The Natural Energy method was applied to different subsamples to define critical periods. Next, a deterministic nonlinear operation optimization model was used to assess the supply to the multiple users for the different critical periods. The main contribution of this study is the impact of nonstationarity in planning and operation of hydrosystems. The results indicated that the natural inflow energy and the stored energy time series are predominantly non-stationary, with a trend change in the 1990s, which modifies the critical period of the basin to 2013-2019, significantly increasing the vulnerability of the system in about 35% when compared to the currently used critical period (1949-1956).
In this paper, an efficient implementation of aggregate homotopy method for nonconvex nonlinear programming problems is proposed. Adopting truncated aggregate technique, only a small subset of the constraints is aggre...
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In this paper, an efficient implementation of aggregate homotopy method for nonconvex nonlinear programming problems is proposed. Adopting truncated aggregate technique, only a small subset of the constraints is aggregated at each iteration, hence the number of gradient and Hessian calculations is reduced dramatically. The subset is adaptively updated with some cheaply implementable truncating criterions, to guarantee the locally quadratic convergence of the correction process with as few computation cost as possible. Numerical tests with comparison to some other methods show that the new method is very efficient, especially for the problems with large amount of constraints and {computationally expensive} gradients or Hessians.
In this paper we consider generalized convexity and concavity properties of the optimal value functionf * for the general parametric optimization problemP(ε) of the form min x f(x, ε) s.t.x∈R(ε). Many results on ...
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In this paper we consider generalized convexity and concavity properties of the optimal value functionf * for the general parametric optimization problemP(ε) of the form min x f(x, ε) s.t.x∈R(ε). Many results on convexity and concavity characterizations off * were presented by the authors in a previous paper. Such properties off * and the solution set mapS * form an important part of the theoretical basis for sensitivity, stability and parametric analysis in mathematical optimization. We give sufficient conditions for several types of generalized convexity and concavity off *, in terms of respective generalized convexity and concavity assumptions onf and convexity and concavity assumptions on the feasible region point-to-set mapR. Specializations of these results to the parametric inequality-equality constrained nonlinear programming problem are provided.
Quite often, engineers obtain measurements associated with several response variables. Both the design and analysis of multi-response experiments with a focus on quality control and improvement have received little at...
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Quite often, engineers obtain measurements associated with several response variables. Both the design and analysis of multi-response experiments with a focus on quality control and improvement have received little attention although they are sorely needed. In a multi-response case the optimization problem is more complex than in the single-response situation. In this paper we present a method to optimize multiple quality characteristics based on the mean square error (MSE) criterion when the data are collected from a combined array. The proposed method will generate more alternative solutions. The string of solutions and the trade-offs aid in determining the underlying mechanism of a system or process. The procedure is illustrated with an example, using the generalized reduced gradient (GRG) algorithm for nonlinear programming. (C) 2007 Elsevier Inc. All rights reserved.
Techniques that identify the active constraints at a solution of a nonlinear programming problem from a point near the solution can be a useful adjunct to nonlinear programming algorithms. They have the potential to i...
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Techniques that identify the active constraints at a solution of a nonlinear programming problem from a point near the solution can be a useful adjunct to nonlinear programming algorithms. They have the potential to improve the local convergence behavior of these algorithms and in the best case can reduce an inequality constrained problem to an equality constrained problem with the same solution. This paper describes several techniques that do not require good Lagrange multiplier estimates for the constraints to be available a priori, but depend only on function and first derivative information. Computational tests comparing the effectiveness of these techniques on a variety of test problems are described. Many tests involve degenerate cases, in which the constraint gradients are not linearly independent and/or strict complementarity does not hold.
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