The performance of gradient methods such as Gauss-Newton method. Davidon-Fletcher-Powell method and modified Successive Linear programming is compared for the solution of identification of dynamic soil properties. The...
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The performance of gradient methods such as Gauss-Newton method. Davidon-Fletcher-Powell method and modified Successive Linear programming is compared for the solution of identification of dynamic soil properties. The identification problem is formulated on the basis of multiple reflection and refraction theory. Through numerical analysis, we showed that modified Successive Linear programming is as good as Gauss-Newton method on the speed of convergence of the solutions, and is superior to others on the property of global convergence.
This paper describes a new algorithm for solving nonlinear programming problems with inequality constraints. The proposed approach first solves a sequence of quadratic programming subproblems with a trust region frame...
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ISBN:
(纸本)9781479947775
This paper describes a new algorithm for solving nonlinear programming problems with inequality constraints. The proposed approach first solves a sequence of quadratic programming subproblems with a trust region framework and to induce global convergence, it establishes a new step acceptance mechanism that is neither a penalty function or a filter. Nonmonotone technique from the unconstraint optimization is used to accelerate the algorithm. Under some reasonable assumptions, the method can be proved to be globally convergent to a KT point. Preliminary numerical experiments are presented that show the potential efficiency of the new approach.
By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constra...
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By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.
A nonlinear programming optimization model was developed to maximize margin over feed cost in broiler feed formulation and is described in this paper. The model identifies the optimal feed mix that maximizes profit ma...
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A nonlinear programming optimization model was developed to maximize margin over feed cost in broiler feed formulation and is described in this paper. The model identifies the optimal feed mix that maximizes profit margin. Optimum metabolizable energy level and performance were found by using Excel Solver nonlinear programming. Data from an energy density study with broilers were fitted to quadratic equations to express weight gain, feed consumption, and the objective function income over feed cost in terms of energy density. Nutrient:energy ratio constraints were transformed into equivalent linear constraints. National Research Council nutrient requirements and feeding program were used for examining changes in variables. The nonlinear programming feed formulation method was used to illustrate the effects of changes in different variables on the optimum energy density, performance, and profitability and was compared with conventional linear programming. To demonstrate the capabilities of the model, I determined the impact of variation in prices. Prices for broiler, corn, fish meal, and soybean meal were increased and decreased by 25%. Formulations were identical in all other respects. Energy density, margin, and diet cost changed compared with conventional linear programming formulation. This study suggests that nonlinear programming can be more useful than conventional linear programming to optimize performance response to energy density in broiler feed formulation because an energy level does not need to be set.
The “cutting plane” method of Kelley for nonlinear programming problems applies linear programming, through a sequence of local linearizations, to the problem of minimizing a convex function of real variables subjec...
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The “cutting plane” method of Kelley for nonlinear programming problems applies linear programming, through a sequence of local linearizations, to the problem of minimizing a convex function of real variables subject to linear inequality constraints. A procedure is presented here for improving the constructed linearizations which may considerably accelerate the convergence of the process. In the case of a quadratic objective function satisfying certain mild conditions this improvement yields a finite algorithm.
The Gamma Knife is a highly specialized treatment unit that provides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. Inside a shielded treatmen...
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The Gamma Knife is a highly specialized treatment unit that provides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. Inside a shielded treatment unit, multiple beams of radiation are focussed into an approximately spherical volume, generating a high dose shot of radiation. The treatment planning process attempts to cover the tumor with sufficient dosage without overdosing normal tissue or surrounding sensitive structures. An optimization problem is formulated that determines where to center the shots, for how long to expose each shot on the target, and what size focussing helmets should be used. We outline a new approach that models the dose distribution nonlinearly, and uses a smoothing approach to treat discrete problem choices. The resulting nonlinear program is not convex and several heuristic approaches are used to improve solution time and quality. The overall approach is fast and reliable;we give several results obtained from use in a clinical setting.
The evaluation of risky assets is one of the major research tasks in the finance theory. There are several Capital Asset Pricing Models (CAPM) in the literature;the most popular one of those is the Sharpe-Lintner-Blac...
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The evaluation of risky assets is one of the major research tasks in the finance theory. There are several Capital Asset Pricing Models (CAPM) in the literature;the most popular one of those is the Sharpe-Lintner-Black mean-variance CAPM. According to this model, the typical measure of systematic risk is the beta coefficient. The beta coefficient can be evaluated by means of least squares method (LSM), Robust Regression Techniques (RRT), or similar approaches. However, the statistical assumptions of LSM might be invalid in the existence of extreme observations in data set. In order to decrease influence on the beta coefficient of extreme observations, most analyst apply to RRT's. However, either RRT's remove the extreme observations from the data set, or decrease their influences on the beta coefficient. Whereas the omitted observations might be valuable for investors since they carry substantial information about the state of nature. In other words, there is a clash between statistical and financial theory. In this study, to overcome this incompatibility, and to take into account the extreme observations carried worthy information, a novel fuzzy regression approach is proposed. The proposed approach is based on both possibility concepts and central tendency in the estimation of beta coefficient. In application section of this paper, the beta coefficients of three assets traded in Istanbul Stock Exchange (ISE) are estimated by the proposed fuzzy approach and the traditional techniques, and then the results of analysis are compared, and discussed. (C) 2012 Elsevier Ltd. All rights reserved.
In this paper we discuss the degeneracy in nonlinear programming with linear constraints, and give a technique for dealing with degeneracy in a general model of reduced gradient algorithms. Under the assumption that t...
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In this paper we discuss the degeneracy in nonlinear programming with linear constraints, and give a technique for dealing with degeneracy in a general model of reduced gradient algorithms. Under the assumption that the objective function is continuously differentiable, we prove that either the iterative sequence {xk} generated by the method terminates at a Kuhn-Tucker point after a finite number of iterations, or any cluster point of the sequence {xk} is a KuhnTucker point.
Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this meth...
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Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this methodology is not efficient because there is no guarantee ensures that one of the chosen values is the best. This encouraged us to look for mathematical method that gives and guarantees the best values of the weighted coefficients. The proposed methodology in this research is to employ the nonlinear programming in determining the weighted coefficients of balanced loss function instead of the unguaranteed old methods. In this research, we consider two balanced loss functions including balanced square error (BSE) loss function and balanced linear exponential (BLINEX) loss function to estimate the parameter and reliability function of inverse Rayleigh distribution (IRD) based on lower record values. Comparisons are made between Bayesian estimators (SE, BSE, LINEX, and BLINEX) and maximum likelihood estimator via Monte Carlo simulation. The evaluation was done based on absolute bias and mean square errors. The outputs of the simulation showed that the balanced linear exponential (BLINEX) loss function has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than corresponding loss function.
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