In this paper Lagrange multipliers are generalized from the usual constants to (possibly nonlinear) multiplier functions. This leads to the statement of several general equivalences results under quite weak assumptions.
In this paper Lagrange multipliers are generalized from the usual constants to (possibly nonlinear) multiplier functions. This leads to the statement of several general equivalences results under quite weak assumptions.
Modeling systems are very important for bringing mathematical programming software to nonexpert users, but few nonlinear programming algorithms are today linked to a modeling system. The paper discussed the advantages...
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Modeling systems are very important for bringing mathematical programming software to nonexpert users, but few nonlinear programming algorithms are today linked to a modeling system. The paper discussed the advantages of linking modeling systems with nonlinear programming. Traditional algorithms can be linked using black-box function and derivatives evaluation routines for local optimization. Methods for generating this information are discussed. More sophisticated algorithms can get access to almost any type of information: interval evaluations and constraint restructuring for detailed preprocessing, second order information for sequential quadratic programming and interior point methods, and monotonicity and convex relaxations for global optimization. Some of the sophisticated information is available today;the rest can be generated on demand. (C) 1997 The Mathematical programming Society, Inc. Published by Elsevier Science B.V.
This paper presents it combined genetic algorithm-fuzzy logic controller (GA-FLC) technique for constrained nonlinear programming problems. In the standard Genetic algorithms, the upper and lower limits of the search ...
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This paper presents it combined genetic algorithm-fuzzy logic controller (GA-FLC) technique for constrained nonlinear programming problems. In the standard Genetic algorithms, the upper and lower limits of the search regions Should be given by the decision maker in advance to the optimization process. In general it needlessly large search region is used in fear of missing the global Optimum Outside the search region. Therefore, if the search region is able to adapt toward a promising area during the optimization process, the performance of GA will be enhanced greatly. Thus in this work we tried to investigate the influence of the bounding intervals on the final result. The proposed algorithm is made of classical GA Coupled with FLC. This controller monitors the variation of the decision variables during process of the algorithm and modifies the boundary intervals to restart the next round of the algorithm. These characteristics make this approach well suited for finding optimal solutions to the highly NLP problems. Compared to previous works on NLP, our method proved to be more efficient in Computation time and accuracy of the final solution. (c) 2005 Elsevier Inc. All rights reserved.
A new approach is described for reducing the number of the fitness and constraint function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables...
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A new approach is described for reducing the number of the fitness and constraint function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed additions to the GA make the search more effective and rapidly improve the fitness value from generation to generation. The additions involve memory as a function of both discrete and continuous design variables and multivariate approximation of the individual functions' responses in terms of several continuous design variables.. W The, approximation is demonstrated for the minimum weight design of a composite cylindrical shell with grid stiffeners.
This article proposes a hybrid optimization algorithm based on a modified BFGS and particle swarm optimization to solve medium scale nonlinear programs. The hybrid algorithm integrates the modified BFGS into particle ...
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This article proposes a hybrid optimization algorithm based on a modified BFGS and particle swarm optimization to solve medium scale nonlinear programs. The hybrid algorithm integrates the modified BFGS into particle swarm optimization to solve augmented Lagrangian penalty function. In doing so, the algorithm launches into a global search over the solution space while keeping a detailed exploration into the neighborhoods. To shed light on the merit of the algorithm, we provide a test bed consisting of 30 test problems to compare our algorithm against two of its variations along with two state-of-the-art nonlinear optimization algorithms. The numerical experiments illustrate that the proposed algorithm makes an effective use of hybrid framework when dealing with nonlinear equality constraints although its convergence cannot be guaranteed. (C) 2012 Elsevier Ltd. All rights reserved.
An articulated figure is often modeled as a set of rigid segments connected with joints. Its configuration can be altered by varying the joint angles. Although it is straightforward to compute figure configurations gi...
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An articulated figure is often modeled as a set of rigid segments connected with joints. Its configuration can be altered by varying the joint angles. Although it is straightforward to compute figure configurations given joint angles (forward kinematics), it is more difficult to find the joint angles for a desired configuration (inverse kinematics). Since the inverse kinematics problem is of special importance to an animator wishing to set a figure to a posture satisfying a set of positioning constraints, researchers have proposed several different approaches. However, when we try to follow these approaches in an interactive animation system where the object on which to operate is as highly articulated as a realistic human figure, they fail in either generality or performance. So, we approach this problem through nonlinear programming techniques. It has been successfully used since 1988 in the spatial constraint system within Jack(R), a human figure simulation system developed at the University of Pennsylvania, and proves to be satisfactorily efficient, controllable, and robust. A spatial constraint in our system involves two parts: one constraint on the figure, the end-effector, and one on the spatial environment, the goat. These two parts are dealt with separately, so that we can achieve a neat modular implementation. Constraints can be added one at a time with appropriate weights designating the importance of this constraint relative to the others and are always solved as a group. If physical limits prevent satisfaction of all the constraints, the system stops with the (possibly local) optimal solution for the given weights. Also, the rigidity of each joint angle can be controlled, which is useful for redundant degrees of freedom.
In this paper, a new set of necessary conditions for optimality is introduced with reference to the differentiable nonlinear programming problem. It is shown that these necessary conditions are sharper than the usual ...
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In this paper, a new set of necessary conditions for optimality is introduced with reference to the differentiable nonlinear programming problem. It is shown that these necessary conditions are sharper than the usual Fritz John ones. A constraint qualification relevant to the new necessary conditions is defined and extensions to the locally Lipschitz case are presented.
In this paper, we outline an algorithm for solving mixed integer nonlinear programming (MINLP) problems. The approach uses a branch-and-bound framework for handling the integer variables and an infeasible interior-poi...
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In this paper, we outline an algorithm for solving mixed integer nonlinear programming (MINLP) problems. The approach uses a branch-and-bound framework for handling the integer variables and an infeasible interior-point method for solving the resulting nonlinear subproblems. We report on the details of the implementation, including the efficient pruning of the branch-and-bound tree via equilibrium constraints, warmstart strategies for interior-point methods, and the handling of infeasible subproblems, and present numerical results on a standard problem library. Our goal is to demonstrate the viability of interior-point methods, with suitable modifications, to be used within any MINLP framework, and the numerical results provided are quite encouraging.
To enhance the performance of the internal due date assignment in a wafer fab even further, this study incorporated the fuzzy c-means-back propagation network (FCM-BPN) approach with a nonlinear programming model. In ...
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To enhance the performance of the internal due date assignment in a wafer fab even further, this study incorporated the fuzzy c-means-back propagation network (FCM-BPN) approach with a nonlinear programming model. In the proposed methodology, the jobs are first classified into several categories by fuzzy c-means. Then, an individual back propagation network is constructed for each category to predict the completion time of the jobs. Subsequently, an individual nonlinear programming model is constructed for each back propagation network to adjust the connection weights in the back propagation network allowing us to determine the internal due dates of the jobs in the category. The nonlinear programming model is finally converted into a goal programming problem that can be solved with existing optimization software. According to the experimental results, the proposed methodology outperforms the baseline multiple linear regression (MLR) approach by 24% in predicting the job completion/cycle times. In addition, the proposed methodology also guarantees that all jobs can be finished before the established internal due dates, without adding too large a fudge factor, and without sacrificing the accuracy of the completion/cycle time forecasts. (C) 2009 Elsevier Ltd. All rights reserved.
Recently, Gulati and Craven and Mond and Egudo established strict converse duality theorems for some of Mond-Weir duals for nonlinear programming problems. Here, we establish various duality theorems under weaker conv...
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Recently, Gulati and Craven and Mond and Egudo established strict converse duality theorems for some of Mond-Weir duals for nonlinear programming problems. Here, we establish various duality theorems under weaker convexity conditions that are different from those of Gulati and Craven, Mond and Weir, and Mond and Egudo.
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