Based on the introduction of some new concepts of semifeasible direction, Feasible Degree (FD1) of semifeasible direction, feasible degree (FD2) of illegal points 'belonging to' feasible domain, etc., this pap...
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Based on the introduction of some new concepts of semifeasible direction, Feasible Degree (FD1) of semifeasible direction, feasible degree (FD2) of illegal points 'belonging to' feasible domain, etc., this paper proposed a new fuzzy method for formulating and evaluating illegal points and three new kinds of evaluation functions and developed a special Hybrid Genetic Algorithm (HGA) with penalty function and gradient direction search for nonlinear programming problems. It uses mutation along the weighted gradient direction as its main operator and uses arithmetic combinatorial crossover only in the later generation process. Simulation of some examples show that this method is effective. (C) 1998 Elsevier Science Ltd. All rights reserved.
We treat the sliding mode control problem by formulating it as a two phase problem consisting of reaching and sliding phases. We show that such a problem can be formulated as bicriteria nonlinear programming problem b...
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We treat the sliding mode control problem by formulating it as a two phase problem consisting of reaching and sliding phases. We show that such a problem can be formulated as bicriteria nonlinear programming problem by associating each of these phases with an appropriate objective function and constraints. We then scalarize this problem by taking weighted sum of these objective functions. We show that by solving a sequence of such formulated nonlinear programming problems it is possible to obtain sliding mode controller feedback coefficients which yield a competitive performance throughout the control. We solve the nonlinear programming problems so constructed by using the modified subgradient method which does not require any convexity and differentiability assumptions. We illustrate validity of our approach by gencrating a sliding mode control input function for stabilization of an inverted pendulum. (c) 2005 Elsevier Inc. All rights reserved.
An adaptive, general-purpose, constraint-solving guidance algorithm has been developed by the authors in response to the requirements for the advanced launch system. The algorithm can be used for all mission phases fo...
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An adaptive, general-purpose, constraint-solving guidance algorithm has been developed by the authors in response to the requirements for the advanced launch system. The algorithm can be used for all mission phases for a wide range of space transportation vehicles without code modification because of the general formulation of the nonlinear programming problem, and the general trajectory simulation used to predict constraint values. The approach allows onboard retargeting for severe weather and changes in payload or mission parameters, increasing flight reliability and dependability, while reducing the amount of preflight analysis that must be performed. The algorithm is described in general in this paper. Three-degree-of-freedom closed-loop simulation results are presented for application of the algorithm to advanced launch system ascent, re-entry of a low lift-to-drag vehicle, and Mars aerobraking. Flight processor throughput requirement data are shown for each of these applications.
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.
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.
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 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.
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.
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.
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