A method for improving local optimal solutions of nonlinear programming problems by treating constraints directly, which is named "Modal Trimming Method", is proposed. This method combines a gradient method ...
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A method for improving local optimal solutions of nonlinear programming problems by treating constraints directly, which is named "Modal Trimming Method", is proposed. This method combines a gradient method for searching local optimal solutions, with an extended Newton-Raphson method based on the Moore-Penrose generalized inverse of a Jacobian matrix of objective and constraint functions for searching initial feasible solutions used by the gradient method. A strategy for preventing traps into fathomed local optimal solutions is proposed. Some features of the method are investigated qualitatively, and it is found that they are suitable to improve local optimal solutions efficiently. The method is applied to a wide range of problems, and its performance is evaluated in terms of the global optimality of the suboptimal solutions. It turns out that the method has a high possibility of deriving the global optimal solutions by the suboptimal ones for a wide range of problems.
This paper analyses the solution of a specific quadratic sub-problem, along with its possible applications, within both constrained and unconstrained nonlinear programming frameworks. We give evidence that this sub-pr...
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This paper analyses the solution of a specific quadratic sub-problem, along with its possible applications, within both constrained and unconstrained nonlinear programming frameworks. We give evidence that this sub-problem may appear in a number of Linesearch Based Methods (LBM) schemes, and to some extent it reveals a close analogy with the solution of trust-region sub-problems. Namely, we refer to a two-dimensional structured quadratic problem, where five linear inequality constraints are included. Finally, we detail how to compute an exact global solution of our two-dimensional quadratic sub-problem, exploiting first order Karush-Khun-Tucker (KKT) conditions.
An exact-penalty-function-based scheme-inspired from an old idea due to Mayne and Polak [Math. Program., 11 ( 1976), pp. 67-80]-is proposed for extending to general smooth constrained optimization problems any given f...
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An exact-penalty-function-based scheme-inspired from an old idea due to Mayne and Polak [Math. Program., 11 ( 1976), pp. 67-80]-is proposed for extending to general smooth constrained optimization problems any given feasible interior-point method for inequality constrained problems. It is shown that the primal-dual interior-point framework allows for a simpler penalty parameter update rule than the one discussed and analyzed by the originators of the scheme in the context of first order methods of feasible direction. Strong global and local convergence results are proved under mild assumptions. In particular, (i) the proposed algorithm does not suffer a common pitfall recently pointed out by Wachter and Biegler [Math. Program., 88 (2000), pp. 565-574];and (ii) the positive definiteness assumption on the Hessian estimate, made in the original version of the algorithm, is relaxed, allowing for the use of exact Hessian information, resulting in local quadratic convergence. Promising numerical results are reported.
Some necessary global optimality conditions and sufficient global optimality conditions for nonconvex minimization problems with a quadratic inequality constraint and a linear equality constraint are derived. In parti...
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Some necessary global optimality conditions and sufficient global optimality conditions for nonconvex minimization problems with a quadratic inequality constraint and a linear equality constraint are derived. In particular, global optimality conditions for nonconvex minimization over a quadratic inequality constraint which extend some known global optimality conditions in the existing literature are presented. Some numerical examples are also given to illustrate that a global minimizer satisfies the necessary global optimality conditions but a local minimizer which is not global may fail to satisfy them.
Abstract Controller synthesis for linear parameter varying (LPV) systems has received a lot of attention from the control community. This is mainly motivated by the wide range of non-linear dynamical systems that can ...
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Abstract Controller synthesis for linear parameter varying (LPV) systems has received a lot of attention from the control community. This is mainly motivated by the wide range of non-linear dynamical systems that can be approximated by LPV-systems. In this paper a novel method is presented that, by only using local state space models as data, tries to solve the problem of finding a linear parameter varying output-feedback controller. The method uses non-linear programming and a quasi-Newton framework to solve the problem. The great advantages with the proposed method is that it is possible to impose structure in the controller and that you do not need an LPV-model, only state space models for different values of the scheduling parameters. Finally an example is presented to show the potential of the method.
Applying fuzzy principles and approaches to the queue systems will provide more extensive and realistic applications of them. A queue system of M/M/c is studied based on fuzzy approach in this paper. This system was p...
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As the core of the effective financial crisis prevention, enterprise finance crisis prediction has been the focal attention of both theorists and businessmen. Financial crisis predictions need to apply a variety of fi...
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As the core of the effective financial crisis prevention, enterprise finance crisis prediction has been the focal attention of both theorists and businessmen. Financial crisis predictions need to apply a variety of financial and operating indicators for its analysis. Therefore, a new evaluation model based on nonlinear programming is established, the nature of the model is proved, the detailed solution steps of the model are given, and the significance and algorithm of the model are thoroughly discussed in this study. The proposed model can deal with the case of missing data, and has the good isotonic property and profound theoretical background. In the empirical analysis to predict the financial crisis and through the comparison of the analysis of historical data and the real enterprises with financial crisis, we find that the results are in accordance with the real enterprise financial conditions and the proposed model has a good predictive ability.
The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush-Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear p...
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The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush-Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear programming problems are derived. Based on the concepts of having no duality gap in weak and strong sense, the Wolfe duality theorems for the invex interval-valued nonlinear programming problems are proposed in this paper.
To reduce the operational cost of district-heating (DH) system on the premise of meeting user’s load, an optimization objective function of operational cost had been proposed, and its variables were supply temperatur...
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The four most successful approaches for solving the constrained nonlinear programming problem are the penalty, multiplier, sequential quadratic programming, and generalized reduced gradient methods. A general algorith...
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The four most successful approaches for solving the constrained nonlinear programming problem are the penalty, multiplier, sequential quadratic programming, and generalized reduced gradient methods. A general algorithmic frame will be presented, which realizes any of these methods only by specifying a search direction for the variables, a multiplier estimate, and some penalty parameters in each iteration. This approach allows one to illustrate common mathematical features and, on the other hand, serves to explain the different numerical performance results we observe in practice.
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