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Nonlinear programming: Algorithms, software, and applications - From small to very large scale optimization

21st Conference on System Modeling and Optimization

作者： Schittkowski, K Zillober, C Univ Bayreuth Dept Comp Sci D-95440 Bayreuth Germany

ISBN: (纸本)1402077602

We introduce some methods for constrained nonlinear programming that are widely used in practice and that are known under the names SQP for sequential quadratic programming and SCP for sequential convex programming. In both cases, convex subproblems are formulated, in the first case a quadratic programming problem, in the second case a separable nonlinear program in inverse variables. The methods are outlined in a uniform way and the results of some comparative performance tests are listed. We especially show the suitability of sequential convex programming methods to solve some classes of very large scale nonlinear programs, where implicitly defined systems of equations seem to support the usage of inverse approximations. The areas of interest are structural mechanical optimization, i.e., topology optimization, and optimal control of partial differential equations after a full discretization. In addition, a few industrial applications and case studies are shown to illustrate practical situations under which the codes implemented by the authors are in use.

关键词： sequential quadratic programming SQP sequential convex programming SCP comparative tests industrial applications topology optimization optimal control of semilinear elliptic equations

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A trust-region algorithm based on global SQP for reactive power optimization

A trust-region algorithm based on global SQP for reactive po...

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2nd International Conference on Electrical and Electronics Engineering (ICEEE 2005)

作者： Zhou, RJ Zhang, YP Yang, HM Changsha Univ Sci & Technol Coll Elect Engn Hunan 410076 Peoples R China

ISBN: (纸本)0780392302

This paper presents a new trust-region algorithm based on global sequential quadratic programming (SQP) for reactive power optimization. This method is not only reliable and accurate which is similar to SQP, but is also global convergent to trust-region search method. To guarantee feasible region of this sub problem is not null, inaccurate direction component decomposed method is adopted to compute trust-region sub problem. In order to avoid the Marotos Effect, the penalty parameter is effectively regulated in Merit Function. This example of the computation shows that this algorithm has global convergence and is fast, accurate and reliable.

关键词： reactive power optimization trust-region method sequential quadratic programming global convergence

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Trajectory planning for multiple robots in bearing-only target localisation

Trajectory planning for multiple robots in bearing-only targ...

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IEEE/RSJ International Conference on Intelligent Robots and Systems

作者： Leung, C Huang, SD Dissanayake, G Furukawa, T Univ Technol Sydney Fac Engn ARC Ctr Excellence Autonomous Syst Sydney NSW 2007 Australia

ISBN: (纸本)0780389123

This paper provides a solution to the optimal trajectory planning problem in target localisation for multiple heterogeneous robots with bearing-only sensors. The objective here is to find robot trajectories that maximise the accuracy of the locations of the targets at a prescribed terminal time. The trajectory planning is formulated as an optimal control problem for a nonlinear system with a gradually identified model and then solved using nonlinear Model Predictive Control (MPC). The solution to the MPC optimisation problem is computed through Exhaustive Expansion Tree Search (EETS) plus sequential quadratic programming (SQP). Simulations were conducted using the proposed methods. Results show that EETS alone performs considerably faster than EETS+SQP with only minor differences in information gain, and that a centralised approach outperforms a decentralised one in terms of information gain. We show that a centralised EETS provides a near optimal solution. We also demonstrate the significance of using a matrix to represent the information gathered.

关键词： bearing only target localisation multi-robot optimal trajectory planning Extended Information Filter Model Predictive Control sequential quadratic programming

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Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. Part I: The Krylov-Schur solver

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2005年第2期27卷 687-713页

作者： Biros, G Ghattas, O NYU Courant Inst Math Sci Dept Comp Sci New York NY 10012 USA Carnegie Mellon Univ Dept Biomed Engn Ultrascale Simulat Lab Pittsburgh PA 15213 USA Carnegie Mellon Univ Dept Civil & Environm Engn Ultrascale Simulat Lab Pittsburgh PA 15213 USA

Large-scale optimization of systems governed by partial differential equations ( PDEs) is a frontier problem in scientific computation. Reduced quasi-Newton sequential quadratic programming (SQP) methods are state-of-the-art approaches for such problems. These methods take full advantage of existing PDE solver technology and parallelize well. However, their algorithmic scalability is questionable;for certain problem classes they can be very slow to converge. In this two-part article we propose a new method for steady-state PDE-constrained optimization, based on the idea of using a full space Newton solver combined with an approximate reduced space quasi-Newton SQP preconditioner. The basic components of the method are Newton solution of the first-order optimality conditions that characterize stationarity of the Lagrangian function;Krylov solution of the Karush - Kuhn - Tucker ( KKT) linear systems arising at each Newton iteration using a symmetric quasi-minimum residual method;preconditioning of the KKT system using an approximate state/decision variable decomposition that replaces the forward PDE Jacobians by their own preconditioners, and the decision space Schur complement ( the reduced Hessian) by a BFGS approximation initialized by a two- step stationary method. Accordingly, we term the new method Lagrange - Newton - Krylov - Schur (LNKS). It is fully parallelizable, exploits the structure of available parallel algorithms for the PDE forward problem, and is locally quadratically convergent. In part I of this two- part article, we investigate the effectiveness of the KKT linear system solver. We test our method on two optimal control problems in which the state constraints are described by the steady-state Stokes equations. The objective is to minimize dissipation or the deviation from a given velocity field;the control variables are the boundary velocities. Numerical experiments on up to 256 Cray T3E processors and on an SGI Origin 2000 include scalability and

关键词： sequential quadratic programming adjoint methods PDE constrained optimization optimal control Lagrange-Newton-Krylov-Schur methods Navier-Stokes finite elements preconditioners indefinite systems nonlinear equations parallel algorithms

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sequential quadratic programming and congestion management

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ELECTRICAL ENGINEERING 2001年第5-6期83卷 243-250页

作者： Brosda, J Handschin, E Univ Dortmund Inst Elect Energy Syst D-44221 Dortmund Germany

This paper presents a basic idea for a congestion management system based on an optimal power flow using the sequential quadratic programming method under the consideration of FACTS-devices. The potential for using this congestion management system in the deregulated market is discussed. An approach for using the balance markets and regulating power markets to resolve congestions is illustrated here. A special focus in the current research is given to the possibility of using FACTS devices included in the OFF as a congestion management system.

关键词： power markets current research sequential quadratic programming Power flow flexible AC transmission systems optimal load flow MANAGEMENT SYSTEMS

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Guidance strategy for radially accelerated trajectories

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JOURNAL OF SPACECRAFT AND ROCKETS 2005年第4期42卷 677-683页

作者： Yamakawa, H Japan Aeroap Explorat Agcy Kanagawa 2298510 Japan

A guidance scheme is proposed for orbital motion under continuous outward radial acceleration that is inversely proportional to the square of the radial distance from the sun. Such an acceleration regime would be realized under the minimagnetospheric plasma propulsion. The maximum attainable radial distance of the outbound trajectory is investigated, and a guidance scheme for achieving this target maximum distance is established under radial acceleration disturbances. The scheme not only provides a control law for continuous radial acceleration but also yields the amount and timing of impulsive maneuvers required to satisfy the guidance requirement at the terminal point.

关键词： Astronomical Unit Space Law Earth Monte Carlo Simulation Low Thrust Propulsion Orbital Period Nonlinear programming Solar Wind Japan Aerospace Exploration Agency sequential quadratic programming

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NONLINEAR MODEL BASED PREDICTIVE CONTROLLER OF A BUCK BOOST CONVERTER

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IFAC Proceedings Volumes 2005年第1期38卷 193-198页

作者： Martín J. Pomar García Julio E. Normey Rico Eduardo Camponogara Depto. de Automação e Sistemas Universidade Federal de Santa Catarina Cx.P. 476 88040-900 Florianópolis SC BRASIL

This paper presents a Nonlinear Model Based Predictive Controller (NMBPC) of a buck-boost converter (BBC). The NMBPC uses a nonlinear prediction of the system outputs based on a discretization of the average continuous model of the BBC, assuming the duty ratio as the control variable. A classical quadratic cost function J is minimized at each sample time using a sequential quadratic programming (SQP) optimization algorithm that guarantees that the obtained control action gives a local optimal value of J . The tuning of the controller parameters is defined to obtain a compromise between performance and robustness. Simulation results in a wide range of the output voltage show that the proposed control strategy yields very fast time responses even under varying load situations.

关键词： Model Based Predictive Control Nonlinear Systems Optimization sequential quadratic programming Buck-Boost Converter

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A COMPARATIVE STUDY OF DETERMINISTIC AND STOCHASTIC OPTIMIZATION METHODS FOR INTEGRATED DESIGN OF PROCESSES

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IFAC Proceedings Volumes 2005年第1期38卷 335-340页

作者： Mario Francisco Silvana Revollar Pastora Vega Rosalba Lamanna Departamento de Informática y Automática. Universidad de Salamanca. Spain Universidad Simón Bolívar. Dpto. Procesos y Sistemas. Caracas 1081A Venezuela

This paper focuses on the application of stochastic (genetic algorithms, simulated annealing) and deterministic (sequential quadratic programming) optimization methods for the Integrated Design of processes considering dynamical non-linear models. Moreover, a hybrid methodology that combines both types of methods is proposed, showing an improvement on performance. Controllability indexes such as disturbance sensitivity gains, the H ∞ norm, and the ISE were considered to obtain optimum disturbance rejection. In order to illustrate and validate our proposal, an activated sludge process with PI schemes is taken. The problem is stated as a multiobjective non-linear optimization problem with non-linear constraints. The application of the mentioned strategies is discussed. The results are encouraging for future application of these techniques to solve synthesis MINLP problems.

关键词： Integrated Design sequential quadratic programming genetic algorithms stochastic optimization controllability

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A computationally efficient feasible sequential quadratic programming algorithm

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SIAM JOURNAL ON OPTIMIZATION 2001年第4期11卷 1092-1118页

作者： Lawrence, CT Tits, AL Alphatech Inc Arlington VA 22201 USA Univ Maryland Dept Elect & Comp Engn College Pk MD 20742 USA Univ Maryland Syst Res Inst College Pk MD 20742 USA

A sequential quadratic programming (SQP) algorithm generating feasible iterates is described and analyzed. What distinguishes this algorithm from previous feasible SQP algorithms proposed by various authors is a reduction in the amount of computation required to generate a new iterate while the proposed scheme still enjoys the same global and fast local convergence properties. A preliminary implementation has been tested and some promising numerical results are reported.

关键词： sequential quadratic programming SQP feasible iterates feasible SQP FSQP

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Dynamic optimization strategies for three-dimensional conflict resolution of multiple aircraft

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2004年第4期27卷 586-594页

作者： Raghunathan, AU Gopal, V Subramanian, D Biegler, LT Samad, T Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA United Technol Res Ctr E Hartford CT 06108 USA Honeywell Inc Honeywell Automat & Control Solut Minneapolis MN 55418 USA

Free flight is an emerging paradigm in air traffic management. Conflict detection and resolution is the heart of any free-flight concept. The problem of optimal cooperative three-dimensional conflict resolution involving multiple aircraft is addressed by the rigorous numerical trajectory optimization methods. The conflict problem is posed as an optimal control problem of finding trajectories that minimize a certain objective function while the safe separation between each aircraft pair is maintained. The initial and final positions of the aircraft are known and aircraft models with detailed nonlinear point-mass dynamics are considered. The protection zone around the aircraft is modeled to be cylindrical in shape. A novel formulation of the cylindrical protection zone is proposed by the use of continuous variables. The optimal control problem is converted to a finite dimensional nonlinear program (NLP) by the use of collocation on finite elements. The NLP is solved by the use of an interior point algorithm that incorporates a novel line search method. A reliable initialization strategy that yields a feasible solution on simple models is also proposed and adapted to detailed models. Several resolution scenarios are illustrated. The practical issue of flyability of the generated trajectories is addressed by the ability of our mathematical programming framework to accommodate detailed dynamic models.

关键词： Commercial Aircraft Nonlinear programming Trajectory Optimization Air Traffic Management Conflict Detection and Resolution Flight Path Angle Heading Angle sequential quadratic programming Drag Coefficient Aircraft Dynamics

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