Using Frank and Wolfe's algorithm, a new interesting nonlinear programming technique has been developed in an attempt to estimate the geometric shape factor of a buried polarized body from a residual self-potentia...
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Using Frank and Wolfe's algorithm, a new interesting nonlinear programming technique has been developed in an attempt to estimate the geometric shape factor of a buried polarized body from a residual self-potential anomaly. Furthermore, the depth, the polarization angle and the electrical dipole moment have also been derived. This algorithm is noted to be robust and its application to SP data converges rapidly towards the optimal solution. The developed technique is tested through studying synthetic data with and without random noise. As a result, the near agreement between the model geometric shape factor and the evaluated one is well recognized. The validity of this proposed technique is tested on a field example from the Ergani Copper district, Turkey. The superiority of the nonlinear programming technique over other recently published methods is shown.
This article considers the five-link spatial mechanism of manipulating robot with revolute and prismatic kinematic pairs. It is shown that making geometric analysis using classical methods is not rational. This articl...
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An algorithm for the direct numerical solution of an optimal control problem is given. The method employs cubic polynomials to represent state variables, linearly interpolates control variables, and uses collocation t...
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An algorithm for the direct numerical solution of an optimal control problem is given. The method employs cubic polynomials to represent state variables, linearly interpolates control variables, and uses collocation to satisfy the differential equations. This representation transforms the optimal control problem to a mathematical programming problem which is solved by sequential quadratic programming. The method is easy to program for a very general trajectory optimization problem and is shown to be very efficient for several sample problems. Results are compared with solutions obtained with other methods.
In response to increased foreign fishing activity near US coasts, the US Coast Guard developed a 0-1 nonlinear programming model of fisheries law enforcement aircraft patrols that identified the level of patrol requir...
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In response to increased foreign fishing activity near US coasts, the US Coast Guard developed a 0-1 nonlinear programming model of fisheries law enforcement aircraft patrols that identified the level of patrol required to maximize the expected value of the patrol effort. The model results were used to address the strategic questions of determining the required resource levels. to provide justification for additional resources in the budget process, and to establish performance guidelines. A nonlinear behavioral model of a fisherman's probability of violation that explicitly accounted for the deterrent effect of the aircraft patrols was the basis for calculating the expected value of a patrol. The model represented a major advance in characterizing program effectiveness for the fisheries law enforcement program, providing, for the first time, a quantified estimate of deterrence and a defensible analytic basis for determining aircraft needs.
Simplicial decomposition is a special version of the Dantzig—Wolfe decomposition principle, based on Carathéodory's theorem. The associated class of algorithms has the following features and advantages: The ...
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Simplicial decomposition is a special version of the Dantzig—Wolfe decomposition principle, based on Carathéodory's theorem. The associated class of algorithms has the following features and advantages: The master and the subprogram are constructed without dual variables; the methods remain therefore well-defined for non-concave objective functions, and pseudo-concavity suffices for convergence to global maxima. The subprogram produces affinely independent sets of feasible generator points defining simplices, which the master program keeps minimal by dropping redundant generator points and finding maximizers in the relative interiors of the resulting subsimplices. The use of parallel subspaces allows the direct application of any unrestricted optimization method in the master program; thus the best unconstrained procedure for any type of objective function can be used to find constrained maximizers for *** paper presents the theory for this class of algorithms, the APL-code of a “demonstration” method and some computational experience with Colville's test problems.
Pseudoconvexity of a function on one set with respect to some other set is defined and duality theorems are proved for nonlinear programming problems by assuming a certain kind of convexity property for a particular l...
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Pseudoconvexity of a function on one set with respect to some other set is defined and duality theorems are proved for nonlinear programming problems by assuming a certain kind of convexity property for a particular linear combination of functions involved in the problem rather than assuming the convexity property for the individual functions as is usually done. This approach generalizes some of the well-known duality theorems and gives some additional strict converse duality theorems which are not comparable with the earlier duality results of this type. Further it is shown that the duality theory for nonlinear fractional programming problems follows as a particular case of the results established here.
This paper proposes a procedure to construct the membership functions of the performance measures in bulk service queuing systems with the arrival rate and service rate are fuzzy numbers. The basic idea is to transfor...
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This paper proposes a procedure to construct the membership functions of the performance measures in bulk service queuing systems with the arrival rate and service rate are fuzzy numbers. The basic idea is to transform a fuzzy queue with bulk service to a family of conventional crisp queues with bulk service by applying the alpha-cut approach. On the basis of alpha-cut representation and the extension principle, a pair of parametric nonlinear programs is formulated to describe that family of crisp bulk service queues, via which the membership functions of the performance measures are derived. To demonstrate the validity of the proposed procedure, two fuzzy queues often encountered in transportation management are exemplified. Since the performance measures are expressed by membership functions rather than by crisp values, they completely conserve the fuzziness of input information when some data of bulk-service queuing systems are ambiguous. Thus the proposed approach for vague systems can represent the system more accurately, and more information is provided for designing queuing systems in real life. By extending to fuzzy environment, the bulk service queuing models would have wider applications. (C) 2004 Elsevier B.V. All rights reserved.
We present a review of available tools for solving mixed integer nonlinear programming problems. Our aim is to give the reader a flavor of the difficulties one could face and to discuss the tools one could use to try ...
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We present a review of available tools for solving mixed integer nonlinear programming problems. Our aim is to give the reader a flavor of the difficulties one could face and to discuss the tools one could use to try to overcome such difficulties.
This paper presents a genetic algorithm and nonlinear programming (GA–NLP) hybrid model to derive steady state optimal reservoir operating policies for a multi-purpose reservoir. In the present study, the objective i...
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When Kuhn and Tucker proved the Kuhn-Tucker theorem in 1950 they launched the theory of nonlinear programming. However, in a sense this theorem had been proven already: In 1939 by W. Karush in a master's thesis, w...
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When Kuhn and Tucker proved the Kuhn-Tucker theorem in 1950 they launched the theory of nonlinear programming. However, in a sense this theorem had been proven already: In 1939 by W. Karush in a master's thesis, which was unpublished;in 1948 by F. John in a paper that was at first rejected by the Duke Mathematical Journal;and possibly earlier by Ostrogradsky and Farkas. The questions of whether the Kuhn-Tucker theorem can be seen as a multiple discovery and why the different occurences of the theorem were so differently received by the mathematical communities are discussed on the basis of a contextualized historical analysis of these works. The significance of the contexts both mathematically and socially for these questions is discussed, including the role played by the military in the shape of Office of Naval Research (ONR) and operations research (OR). (C) 2000 Academic Press MSC 1991 subject classification: 01A60;49-03;52-03;90-03;90C30.
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