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A decomposition method based on SQP for a class of multistage stochastic nonlinear programs

SIAM JOURNAL ON OPTIMIZATION 2003年第1期14卷 200-222页

作者： Liu, XW Zhao, GY Natl Univ Singapore Singapore MIT Alliance Singapore 117576 Singapore Natl Univ Singapore Dept Math Singapore 119260 Singapore

Multistage stochastic programming problems arise in many practical situations, such as production and manpower planning, portfolio selections, and so on. In general, the deterministic equivalents of these problems can be very large and may not be solvable directly by general-purpose optimization approaches. sequential quadratic programming (SQP) methods are very effective for solving medium-size nonlinear programming. By using the scenario analysis technique, a decomposition method based on SQP for solving a class of multistage stochastic nonlinear programs is proposed, which generates the search direction by solving parallelly a set of quadratic programming subproblems with much less size than the original problem at each iteration. Conjugate gradient methods can be introduced to derive the estimates of the dual multiplier associated with the nonanticipativity constraints. By selecting the step-size to reduce an exact penalty function sufficiently, the algorithm terminates finitely at an approximate optimal solution to the problem with any desirable accuracy. Some preliminary numerical results are reported.

关键词： multistage stochastic nonlinear programs sequential quadratic programming scenario analysis decomposition

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Stabilized sequential quadratic programming

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 1999年第1-3期12卷 253-273页

作者： Hager, WW Univ Florida Dept Math Gainesville FL 32611 USA

Recently, Wright proposed a stabilized sequential quadratic programming algorithm for inequality constrained optimization. Assuming the Mangasarian-Fromovitz constraint qualification and the existence of a strictly positive multiplier (but possibly dependent constraint gradients), he proved a local quadratic convergence result. In this paper, we establish quadratic convergence in cases where both strict complementarity and the Mangasarian-Fromovitz constraint qualification do not hold. The constraints on the stabilization parameter are relaxed, and linear convergence is demonstrated when the parameter is kept fixed. We show that the analysis of this method can be carried out using recent results for the stability of variational problems.

关键词： sequential quadratic programming quadratic convergence superlinear convergence degenerate optimization stabilized SQP error estimation

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Numerical approximation of an SQP-type method for parameter identification

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SIAM JOURNAL ON NUMERICAL ANALYSIS 2002年第5期40卷 1775-1797页

作者： Burger, M Mühlhuber, W Johannes Kepler Univ Linz SFB Numer & Symbol Sci Comp F 013 A-4040 Linz Austria

This paper deals with the numerical approximation of the Levenberg-Marquardt SQP (LMSQP) method for parameter identification problems, which has been presented and analyzed in [M. Burger and W. Muhlhuber, Inverse Problems, 18 (2002), pp. 943-969]. It is shown that a Galerkin-type discretization leads to a convergent approximation and that the indefinite system arising from the Karush-Kuhn-Tucker (KKT) system is well-posed. In addition, we present a multilevel version of the Levenberg Marquardt method and discuss the simultaneous solution of the discretized KKT system by preconditioned iteration methods for indefinite problems. From a discussion of the numerical effort we conclude that these approaches may lead to a considerable speed-up with respect to standard iterative regularization methods that eliminate the underlying state equation. The numerical efficiency of the LMSQP method is confirmed by numerical examples.

关键词： parameter identification sequential quadratic programming iterative regularization Galerkin methods indefinite systems

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Structural shape optimization using MSC/NASTRAN and sequential quadratic programming

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COMPUTERS & STRUCTURES 1999年第5期70卷 487-514页

作者： Holzleitner, L Mahmoud, KG Siemens AG PSE A-1100 Vienna Austria AVL List GmbH A-8020 Graz Austria

This work is a continuation of a work done by the authors on sizing optimization where the structure is optimized with respect to the thickness. In this work shape optimization is performed. The implementation is described and a comparison has been made between three different methods for sensitivity analysis calculation. An efficient coupling with an optimization module and the commercial finite element package MSC/NASTRAN using DMAP (direct matrix abstraction program) is made. A sequential quadratic programming algorithm is used for optimization. Differences in the implementation of these sensitivity analysis methods as well as advantages and disadvantages are outlined. In order to give a practical comparison between the three methods and to demonstrate the feasibility of the proposed methodology, the shape optimization of a disk with a hole at the center and a unit injector rocker arm are presented as examples. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： finite element structural optimization shape optimization sensitivity analysis adjoint method for sensitivity analysis sequential quadratic programming

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Optimal operation of a hospital power plant

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ENERGY AND BUILDINGS 2002年第10期34卷 1055-1065页

作者： van Schijndel, AWM Eindhoven Univ Technol Dept Architecture Bldg Grp Bldg Phys FAGO NL-5600 MB Eindhoven Netherlands

In this paper the operation of an Academic Hospital installation is evaluated by simulation and optimization on a yearly base. A mathematical model has been developed, which is based on energy balances of the installed components. Manufacturer specifications of the components are used for calculating the parameters. The model is formulated using vector equations. Advantages of this type of model formulations are presented. The tools used for optimization are custom developed back-tracking methods for calculating a good starting point and a SQP optimization tool for finding the optimum. Detailed control strategies are calculated for three types of optimization strategies simulated. The simulation results show the impact of the choice of a control strategy on the optimized operation. The results are also applicable for on-line setpoint optimization. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： absorption chiller sequential quadratic programming combined heat and power

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Lessons learned during solutions of multidisciplinary design optimization problems

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JOURNAL OF AIRCRAFT 2002年第3期39卷 386-393页

作者： Patnaik, SN Coroneos, RM Hopkins, DA Lavelle, TM Ohio Aersp Inst Brookpark OH 44142 USA NASA John H Glenn Res Ctr Cleveland OH 44135 USA

Optimization research at NASA Glenn Research Center has addressed design of structures, aircraft, and aircraft engines. Four issues were encountered during the solution of the multidisciplinary problems. Strategy adapted for their resolution is discussed. Design optimization produced an inefficient design for an engine component. The deficiency was overcome through animation and weight was reduced by 20%. Infeasibility encountered in aircraft and engine design problems was alleviated by cascading multiple algorithms. The cascade strategy reduced aircraft weight and produced a feasible design. Profile optimization converged to an irregular shape for a beam. A regular shape was restored through engineering intuition, but the optimum freight was not changed. The subproblem optimization for a cylindrical shell converged to a design that might be difficult to manufacture. This issue remains a challenge. The issues are illustrated through design of an engine component, synthesis of a subsonic aircraft, operation optimization of a supersonic engine, design of a wave-rotor-topping device, profile optimization of a beam, and design of a cylindrical shell. A multidisciplinary problem might not Yield an optimum solution in the first attempt. However, the combined effort of designers and researchers can bring design optimization from academia to industry.

关键词： Multidisciplinary Design Optimization Supersonic Aircraft Cylindrical Shells Overall Pressure Ratio NASA Glenn Research Center Aircraft Engine Design sequential quadratic programming High Pressure Turbine Poisson's Ratio Airbreathing Propulsion

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Reduced-order entry trajectory planning for acceleration guidance

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2002年第2期25卷 257-266页

作者： Mease, KD Chen, DT Teufel, P Schönenberger, H Univ Calif Irvine Dept Mech & Aerosp Engn Irvine CA 92697 USA Univ Stuttgart Dept Mech & Aerosp Engn D-7000 Stuttgart Germany Univ Stuttgart Inst Flight Mech & Control D-7000 Stuttgart Germany

The acceleration guidance concept is to plan an aerodynamic acceleration profile that integrates to the desired final position and velocity and satisfies all vehicle constraints and to track the acceleration profile. The longitudinal entry guidance for the space shuttle is acceleration guidance: a drag deceleration profile that integrates to the desired downrange and satisfies the vehicle constraints is planned and tracked primarily by bank-angle adjustments. The kinematics relating the drag profile to the downrange assume that the entry trajectory is a great circle arc. In this paper we consider lateral as well as longitudinal motion in acceleration planning. Three differential equations that are the kinematic relations between the aerodynamic accelerations and the position and velocity variables with energy as the independent variable are used as the basis for two methods of planning the drag and lateral acceleration profiles. The first is simpler and produces a feasible trajectory for a given angle-of-attack profile. The second requires more computation, but produces an optimal trajectory using both angle-of-attack and angle-of-bank variations to control the entry trajectory and has greater capability to shape the entry trajectory. Both methods are demonstrated using an X-33 vehicle model. The optimal method is capable of achieving a specified final heading angle and adjusting the number of bank reversals.

关键词： Angle of Attack Heading Angle Lift Forces Space Shuttle Closed Loop Optimal Control Earth Nonlinear programming Dynamic Pressure sequential quadratic programming

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Dynamic optimal control of batch rice drying process

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DRYING TECHNOLOGY 2002年第7期20卷 1319-1345页

作者： Olmos, A Trelea, IC Courtois, F Bonazzi, C Trystram, G INAPG INRA ENSIA CemagrefUMR Genie Ind AlimentaireENSIA F-91744 Massy France INA PG UMR Genie & Microbiol Procedes Alimentaires F-78850 Thiverval Grignon France

The drying of paddy rice may result in quality degradation, expressed as a head kernel yield, leading to significant commercial depreciation of the product. A mathematical model of the drying and of the quality degradation process was combined with a dynamic optimization algorithm to determine the drying conditions (air temperature and relative humidity as functions of time) that ensured the highest possible final product quality for a specified drying time and a specified final moisture content. The robustness of the optimal drying strategy with respect to the initial state of the product, to the model parameters and to the initialization of the optimization algorithm was verified. The compromise between the highest achievable final quality and the allowed total drying time was studied. The combination of simulation and optimization yielded a new insight in the rice drying process and in the quality preservation strategies.

关键词： grain breakage dynamic optimization optimal control paddy rice drying sequential quadratic programming

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Nonmonotone line search algorithm for constrained minimax problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2002年第2期115卷 419-446页

作者： Yu, YH Gao, L Peking Univ Sch Math Sci Beijing 100871 Peoples R China

In this paper, an algorithm for constrained minimax problems is presented which is globally convergent and whose rate of convergence is two-step superlinear. The algorithm applies SQP to the constrained minimax problems by combining a nonmonotone line search and a second-order correction technique, which guarantees a full steplength while close to a solution, such that the Maratos effect is avoided and two-step superlinear convergence is achieved.

关键词： constrained minimax problems sequential quadratic programming Maratos effect nonmonotone line search superlinear convergence

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Parallel variable distribution for constrained optimization

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2002年第1期22卷 111-131页

作者： Sagastizábal, CA Solodov, MV INRIA Rocquencourt F-78153 Le Chesnay France Inst Matematica Pura & Aplicada BR-22460320 Rio De Janeiro Brazil

In the parallel variable distribution framework for solving optimization problems (PVD), the variables are distributed among parallel processors with each processor having the primary responsibility for updating its block of variables while allowing the remaining "secondary" variables to change in a restricted fashion along some easily computable directions. For constrained nonlinear programs convergence theory for PVD algorithms was previously available only for the case of convex feasible set. Additionally, one either had to assume that constraints are block-separable, or to use exact projected gradient directions for the change of secondary variables. In this paper, we propose two new variants of PVD for the constrained case. Without assuming convexity of constraints, but assuming block-separable structure, we show that PVD subproblems can be solved inexactly by solving their quadratic programming approximations. This extends PVD to nonconvex (separable) feasible sets, and provides a constructive practical way of solving the parallel subproblems. For inseparable constraints, but assuming convexity, we develop a PVD method based on suitable approximate projected gradient directions. The approximation criterion is based on a certain error bound result, and it is readily implementable. Using such approximate directions may be especially useful when the projection operation is computationally expensive.

关键词： parallel optimization variable distribution constrained optimization sequential quadratic programming projected gradient

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