An initial value determination method with a contraction factor for the counter-pumped Raman coupled equations is proposed. This method is used in conjunction with initial guess correction mechanism of Newton's me...
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An initial value determination method with a contraction factor for the counter-pumped Raman coupled equations is proposed. This method is used in conjunction with initial guess correction mechanism of Newton's method to construct a new efficient shooting algorithm for the solution of counter-pumped Raman coupled equations. The particle swarm optimization is used to find the optimal wavelengths and powers for the pumps. By combining the new shooting algorithm and particle swarm optimization a powerful approach to the design of gain spectra for Raman fiber amplifiers is developed. Using this approach a counter-pumped broadband Raman fiber amplifier in C + L-band is designed and optimized. An average on-off gain of 9.3 dB for a bandwidth of 95 nm is obtained using only 4 pumps, with an in-band ripple level of +/-0.7 dB. (C) 2010 Elsevier B.V. All rights reserved.
We develop an efficient allocation-based solution framework for a class of two-facility location-allocation problems with dense demand data. By formulating the problem as a multi-dimensional boundary value problem, we...
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We develop an efficient allocation-based solution framework for a class of two-facility location-allocation problems with dense demand data. By formulating the problem as a multi-dimensional boundary value problem, we show that previous results for the discrete demand case can be extended to problems with highly dense demand data. Further, this approach can be generalized to non-convex allocation decisions. This formulation is illustrated for the Euclidean metric case by representing the affine bisector with two points. A specialized multi-dimensional shooting algorithm is presented and illustrated on an example. Comparisons with two alternative methods through a computational study confirm the efficiency of the proposed methodology. (C) 2010 Elsevier Ltd. All rights reserved.
This paper deals with the shooting algorithm for optimal control problems with a scalar control and a regular scalar state constraint. Additional conditions are displayed, under which the so-called alternative formula...
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This paper deals with the shooting algorithm for optimal control problems with a scalar control and a regular scalar state constraint. Additional conditions are displayed, under which the so-called alternative formulation is equivalent to Pontryagin's minimum principle. The shooting algorithm appears to be well-posed (invertible Jacobian) iff (i) the no-gap second-order sufficient optimality condition holds, and (ii) when the constraint is of order q >= 3, there is no boundary arc. Stability and sensitivity results without strict complementarity at touch points are derived using Robinson's strong regularity theory, under a minimal second-order sufficient condition. The directional derivatives of the control and state are obtained as solutions of a linear quadratic problem.
This paper describes the development of an exact allocation-based solution algorithm for the facility location and capacity acquisition problem (LCAP) on a line with dense demand data. Initially, the n-facility proble...
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This paper describes the development of an exact allocation-based solution algorithm for the facility location and capacity acquisition problem (LCAP) on a line with dense demand data. Initially, the n-facility problem on a line is studied and formulated as a dynamic programming model in the allocation decision space. Next, we cast this dynamic programming formulation as a two-point boundary value problem and provide conditions for the existence and uniqueness of solutions. We derive sufficient conditions for non-empty service regions and necessary conditions for interior facility locations. We develop an efficient exact shooting algorithm to solve the problem as an initial value problem and illustrate on an example. A computational study is conducted to study the effect of demand density and other problem parameters on the solutions. (C) 2016 Elsevier Ltd. All rights reserved.
We deal with a control-affine problem with scalar control subject to bounds, a scalar state constraint and endpoint constraints of equality type. For the numerical solution of this problem, we propose a shooting algor...
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We deal with a control-affine problem with scalar control subject to bounds, a scalar state constraint and endpoint constraints of equality type. For the numerical solution of this problem, we propose a shooting algorithm and provide a sufficient condition for its local convergence. We exhibit an example that illustrates the theory.
In this article, we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and ...
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In this article, we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent, if the derivative of the shooting function is one-to-one at the solution. The main result of this paper is to show that the latter holds whenever a sufficient condition for weak optimality is satisfied. We note that this condition is very close to a second order necessary condition. For the case when the shooting system can be reduced to one having the same number of unknowns and equations (square system), we prove that the mentioned sufficient condition guarantees the stability of the optimal solution under small perturbations and the invertibility of the Jacobian matrix of the shooting function associated with the perturbed problem. We present numerical tests that validate our method.
In this article we propose a shooting algorithm for optimal control problems governed by systems that are affine in one part of the control variable. Finitely many equality constraints on the initial and final state a...
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ISBN:
(纸本)9783033039629
In this article we propose a shooting algorithm for optimal control problems governed by systems that are affine in one part of the control variable. Finitely many equality constraints on the initial and final state are considered. We recall a second order sufficient condition for weak optimality, and show that it guarantees the local quadratic convergence of the algorithm. We show an example and solve it numerically.
In this study, an incompressible, steady, and magnetohydrodynamic flow of Buongiorno nanofluid through a stretchable surface has been analyzed by adopting a theoretical and numerical approach. This paper involves the ...
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In this study, an incompressible, steady, and magnetohydrodynamic flow of Buongiorno nanofluid through a stretchable surface has been analyzed by adopting a theoretical and numerical approach. This paper involves the impacts of buoyancy forces, thermal conductivity, chemically diffusion, and Arrhenius activation energy. Moreover, the influence of the suspension of gyrotactic microorganisms in the nanofluids is also a part of this study. It is assumed that the behavior of viscosity varies as a function of time and the suspension of microorganisms remain consistent throughout the study. A system of PDEs is reduced to a solvable system of ODEs by applying a suitable similarity transformation. For the sake of numerical solutions, the shooting method has been employed. Wolfram Mathematica has been used to deal with the BVP. In addition, the behaviors of different emerging parameters comprising velocity outline, temperature outline, concentration distribution, the density outline of gyrotactic microorganisms have also been demonstrated by graphical illustrations. From the extracted results, it has been observed that the rising values of viscosity of fluid produce a decline in the velocity parameter. Also, an increment has been noticed in the temperature profile for the growing behavior of the mixed convective factor.
A novel method with automatic step-size adjustment for propagation equation calculations in fiber Raman amplifiers is proposed, for the first time to authors' knowledge, in this paper. An effective shooting algori...
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A novel method with automatic step-size adjustment for propagation equation calculations in fiber Raman amplifiers is proposed, for the first time to authors' knowledge, in this paper. An effective shooting algorithm for the two-point boundary value problem is also constructed. Numerical results demonstrate that the computing speed of the proposed method is increased more than four times by comparison with the classical Runge-Kutta-Fehlberg method, the step-size is extended greatly, and the stability is improved. Simulation results also show that the new shooting algorithm can be used to solve Raman amplifier propagation equations on various conditions including co-, counter- and bi-directional pump schemes. (C) 2004 Elsevier B.V. All rights reserved.
This paper deals with optimal control problems with a regular second-order state constraint and a scalar control, satisfying the strengthened Legendre-Clebsch condition. We study the stability of structure of stationa...
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This paper deals with optimal control problems with a regular second-order state constraint and a scalar control, satisfying the strengthened Legendre-Clebsch condition. We study the stability of structure of stationary points. It is shown that under a uniform strict complementarity assumption, boundary arcs are stable under sufficiently smooth perturbations of the data. On the contrary, nonreducible touch points are not stable under perturbations. We show that under some reasonable conditions, either a boundary arc or a second touch point may appear. Those results allow us to design an homotopy algorithm which automatically detects the structure of the trajectory and initializes the shooting parameters associated with boundary arcs and touch points.
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