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shooting algorithm and particle swarm optimization based Raman fiber amplifiers gain spectra design

OPTICS COMMUNICATIONS 2010年第17期283卷 3348-3352页

作者： Jiang, Hai-ming Xie, Kang Wang, Ya-fei Univ Elect Sci & Technol China Sch Optoelect Informat Chengdu 610054 Peoples R China

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.

关键词： Raman fiber amplifier shooting algorithm Particle swarm optimization Gain spectrum Contraction factor Newton's method

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A multi-dimensional shooting algorithm for the two-facility location-allocation problem with dense demand

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COMPUTERS & OPERATIONS RESEARCH 2011年第2期38卷 450-463页

作者： Murat, Alper Verter, Vedat Laporte, Gilbert Wayne State Univ Dept Ind & Mfg Engn Detroit MI 48202 USA McGill Univ Desautels Fac Management Montreal PQ H3A 1G5 Canada HEC Montreal Canada Res Chair Distribut Management Montreal PQ H3T 2A7 Canada

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.

关键词： Location-allocation problem Continuous modeling Boundary value problem shooting algorithm

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Well-posedness of the shooting algorithm for state constrained optimal control problems with a single constraint and control

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2007年第4期46卷 1398-U1页

作者： Bonnans, J. Frederic Hermant, Audrey Ecole Polytech INRIA Futurs CMAP F-91128 Palaiseau France

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.

关键词： optimal control Pontryagin's principle state constraints junction conditions shooting algorithm no-gap second-order optimality conditions strong regularity sensitivity analysis directional derivatives

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A global shooting algorithm for the facility location and capacity acquisition problem on a line with dense demand

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COMPUTERS & OPERATIONS RESEARCH 2016年 71卷 1-15页

作者： Murat, Alper Laporte, Gilbert Verter, Vedat Wayne State Univ Dept Ind & Syst Engn Detroit MI 48202 USA HEC Montreal Distribut Management 3000 Chemin Cote Ste Catherine Montreal PQ H3T 2A7 Canada McGill Univ Desautels Fac Management 1001 Sherbrooke St West Montreal PQ H3A 1G5 Canada

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.

关键词： Location-allocation problem Capacity acquisition Dynamic programming shooting algorithm

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Well-posedness of the shooting algorithm for control-affine problems with a scalar state constraint

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COMPUTATIONAL & APPLIED MATHEMATICS 2023年第5期42卷 1-22页

作者： Aronna, M. Soledad Bonnans, J. Frederic San Goh, Bean FGV EMAp Escola Matemat Aplicada Praia Botafogo 190 BR-22250900 Rio De Janeiro Brazil Cent Supelec INRIA Saclay L2S F-91190 Gif Sur Yvette France Curtin Univ Sch Elect Engn Comp & Math Sci Perth 6845 Australia

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.

关键词： Optimal control shooting algorithm Singular arc Second order optimality conditions

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A shooting algorithm for Optimal Control Problems with Singular Arcs

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2013年第2期158卷 419-459页

作者： Aronna, M. Soledad Bonnans, J. Frederic Martinon, Pierre Univ Padua ITN Marie Curie Network SADCO Padua Italy INRIA Saclay Palaiseau France CMAP Ecole Polytech Palaiseau France

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.

关键词： Optimal control Singular arc Bang-singular control shooting algorithm Second order optimality condition Gauss-Newton method Stability analysis

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Convergence of the shooting algorithm for singular optimal control problems

Convergence of the shooting algorithm for singular optimal c...

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European Control Conference (ECC)

作者： Aronna, M. Soledad Univ London Imperial Coll Sci Technol & Med Network SADCO Dept Elect & Elect Engn London SW7 2AZ England

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.

关键词： optimal control singular control second order optimality condition weak optimality shooting algorithm Gauss-Newton method

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Buoyancy force and Arrhenius energy impacts on Buongiorno electromagnetic nanofluid flow containing gyrotactic microorganism

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 2022年第17期236卷 9459-9471页

作者： Safdar, Rabia Gulzar, Iqra Jawad, Muhammad Jamshed, Wasim Shahzad, Faisal Eid, Mohamed R. Lahore Coll Women Univ Dept Math Lahore Pakistan Univ Faisalabad Sch Management Studies Faisalabad Pakistan Capital Univ Sci & Technol CUST Dept Math Islamabad Pakistan New Valley Univ Fac Sci Dept Math Al Kharga 72511 Al Wadi Al Gadi Egypt Northern Border Univ Fac Sci Dept Math Ar Ar 1321 Saudi Arabia

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.

关键词： gyrotactic microorganisms Arrhenius activation energy chemical diffusion magnetohydrodynamics shooting algorithm Buongiorno nanofluid

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An effective method for two-point boundary value problems in Raman amplifier propagation equations

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OPTICS COMMUNICATIONS 2004年第1-3期235卷 75-82页

作者： Liu, XM Zhang, MD Tsing Hua Univ Dept Elect Engn Beijing 100084 Peoples R China Southeast Univ Dept Elect Engn Nanjing 210096 Peoples R China

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.

关键词： Raman amplifiers two-point boundary value problems ordinary differential equations shooting algorithm Runge-Kutta-Fehlberg

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Homotopy algorithm for Optimal Control Problems with a Second-order State Constraint

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APPLIED MATHEMATICS AND OPTIMIZATION 2010年第1期61卷 85-127页

作者： Hermant, Audrey INRIA Saclay Ile de France Ecole Polytech CMAP F-91128 Palaiseau France

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.

关键词： Optimal control Second-order state constraint Stability analysis shooting algorithm Homotopy method

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