In this note we give an elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints. The proof avoids the impl...
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In this note we give an elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints. The proof avoids the implicit function theorem usually applied when dealing with equality constraints and uses a generalization of Farkas lemma and the Bolzano-Weierstrass property for compact sets. (c) 2006 Elsevier B.V. All rights reserved.
Tendon sheath mechanism (TSM) is an essential mechanical element for the implementation of flexible endoscopic systems owing to its small volume and simple structure. However, nonlinear characteristics, such as backla...
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Tendon sheath mechanism (TSM) is an essential mechanical element for the implementation of flexible endoscopic systems owing to its small volume and simple structure. However, nonlinear characteristics, such as backlash, hysteresis and friction occur when employing such a component. In this study, we formulate a Preisach hysteresis model consisting of elementary hysteresis operators. Subsequently, we propose a compensation algorithm that repeatedly and sequentially solves a nonlinear optimization problem online, producing an inverse control signal for the desired output at every time step, compensating the nonlinear effects of TSM. The results indicate that the presented model and control scheme are promising for motion control in any application utilizing TSM.
We study the performance of some rank-two ellipsoid algorithms when used to solve nonlinear programming problems. Experiments are reported which show that the rank-two algorithms studied are slightly less efficient th...
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We study the performance of some rank-two ellipsoid algorithms when used to solve nonlinear programming problems. Experiments are reported which show that the rank-two algorithms studied are slightly less efficient than the usual rank-one (center-cut) algorithm. Some results are also presented concerning the growth of ellipsoid asphericity in rank-one and rank-two algorithms.
Abstract: Problems are considered in which an objective function expressible as a max of finitely many ${C^2}$ functions, or more generally as the composition of a piecewise linear-quadratic function with a ${...
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Abstract: Problems are considered in which an objective function expressible as a max of finitely many ${C^2}$ functions, or more generally as the composition of a piecewise linear-quadratic function with a ${C^2}$ mapping, is minimized subject to finitely many ${C^2}$ constraints. The essential objective function in such a problem, which is the sum of the given objective and the indicator of the constraints, is shown to be twice epi-differentiable at any point where the active constraints (if any) satisfy the Mangasarian-Fromovitz qualification. The epi-derivatives are defined by taking epigraphical limits of classical first-and second-order difference quotients instead of pointwise limits, and they reveal properties of local geometric approximation that have not previously been observed.
We propose and analyze a primal-dual interior point method of the "feasible" type, with the additional property that the objective function decreases at each iteration. A distinctive feature of the method is...
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We propose and analyze a primal-dual interior point method of the "feasible" type, with the additional property that the objective function decreases at each iteration. A distinctive feature of the method is the use of different barrier parameter values for each constraint, with the purpose of better steering the constructed sequence away from non-KKT stationary points. Assets of the proposed scheme include relative simplicity of the algorithm and of the convergence analysis, strong global and local convergence properties, and good performance in preliminary tests. In addition, the initial point is allowed to lie on the boundary of the feasible set.
The location of the sharp interface between saltwater and freshwater in a coastal aquifer is determined using optimization techniques. The algorithm is based on the combination of a nonlinear programming and an h-adap...
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The location of the sharp interface between saltwater and freshwater in a coastal aquifer is determined using optimization techniques. The algorithm is based on the combination of a nonlinear programming and an h-adaptive boundary element method. The objective is to create an automated solution procedure. The effectiveness of the model is demonstrated using several examples in confined and unconfined aquifers. The unconfined aquifer cases require the simultaneous determination of an interface and a free surface. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.
In a recent paper, Birgin, Floudas and Martinez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the BB method and convergence to ...
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In a recent paper, Birgin, Floudas and Martinez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the BB method and convergence to global minimizers was obtained assuming feasibility of the original problem. In the present research, the algorithm mentioned above will be improved in several crucial aspects. On the one hand, feasibility of the problem will not be required. Possible infeasibility will be detected in finite time by the new algorithms and optimal infeasibility results will be proved. On the other hand, finite termination results that guarantee optimality and/or feasibility up to any required precision will be provided. An adaptive modification in which subproblem tolerances depend on current feasibility and complementarity will also be given. The adaptive algorithm allows the augmented Lagrangian subproblems to be solved without requiring unnecessary potentially high precisions in the intermediate steps of the method, which improves the overall efficiency. Experiments showing how the new algorithms and results are related to practical computations will be given.
Algorithms for solving multiple criteria nonlinear programming problems are frequently based on the use Of the generalized reduced gradient (GRG) method. Since the GRG method gives complex and large size processing fo...
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Algorithms for solving multiple criteria nonlinear programming problems are frequently based on the use Of the generalized reduced gradient (GRG) method. Since the GRG method gives complex and large size processing for computation, it takes much time to solve large-scale multiple criteria nonlinear programming problems. Therefore, parallel processing dealing with the GRG method is required to solve the problems. We propose a parallel processing algorithm for the GRG method under multiple processors systems.
In many papers on the application of nonlinear programming techniques to the solution of engineering problems, such as an induction-motor design, the sequential unconstrained minimisation technique is adopted. It is s...
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In many papers on the application of nonlinear programming techniques to the solution of engineering problems, such as an induction-motor design, the sequential unconstrained minimisation technique is adopted. It is shown in the paper that a nonsequential approach will lead to the same end results with much less computational time. In addition it is shown that a considerable saving in computational time could be achieved in transformer design optimisation by considering the whole problem to consist of a single constraint such as the cost function, with the sum of all suitably weighted constraints on the design performances being brought under the objective function evaluation.
In this paper a class of augmented Lagrangians is considered, for solving equality constrained nonlinear optimization problems via unconstrained minimization techniques. This class of augmented Lagrangians is obtained...
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In this paper a class of augmented Lagrangians is considered, for solving equality constrained nonlinear optimization problems via unconstrained minimization techniques. This class of augmented Lagrangians is obtained by multiplying the penalty term on the first order necessary optimality condition in a class of augmented Lagrangians of Di Pillo and Grippo by a penalty parameter. Under suitable assumptions, the exactly corresponding relationship is established between the solution of the original constrained problem and the unconstrained minimization of this class of augmented Lagrangians on the product space of problem variables and multipliers for sufficiently large but finite values of penalty parameters. Therefore, a solution of the original constrained problem and the corresponding values of the Lagrange multipliers can be found by performing a single unconstrained minimization of an augmented Lagrangian on the product space of problem variables and multipliers. In particular, for quadratic programming problerns with equality constraints,. the optimizer is obtained by minimizing a quadratic function on the expanded space. (c) 2005 Elsevier Inc. All rights reserved.
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