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A filter sequential adaptive cubic regularization algorithm for nonlinear constrained optimization

NUMERICAL ALGORITHMS 2023年第4期93卷 1481-1507页

作者： Pei, Yonggang Song, Shaofang Zhu, Detong Henan Normal Univ Coll Math & Informat Sci Engn Lab Big Data Stat Anal & Optimal Control Construct Rd Xinxiang 453007 Henan Peoples R China Shanghai Normal Univ Math & Sci Coll Guilin Rd Shanghai 200234 Peoples R China

In this paper, we propose a filter sequential adaptive regularization algorithm using cubics (ARC) for solving nonlinear equality constrained optimization. Similar to sequential quadratic programming methods, an ARC subproblem with linearized constraints is considered to obtain a trial step in each iteration. Composite step methods and reduced Hessian methods are employed to tackle the linearized constraints. As a result, a trial step is decomposed into the sum of a normal step and a tangential step which is computed by a standard ARC subproblem. Then, the new iteration is determined by filter methods and ARC framework. The global convergence of the algorithm is proved under some reasonable assumptions. Preliminary numerical experiments and comparison results are reported.

关键词： Nonlinear constrained optimization Cubic regularization Filter methods sequential quadratic programming Global convergence

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Nonlinear Model Predictive Control of a Distillation Column Using Wavenet Based Hammerstein Model

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ENGINEERING LETTERS 2012年第4期20卷 330-335页

作者： Ramesh, K. Hisyam, A. Aziz, N. Shukor, S. R. Abd Univ Malaysia Pahang Fac Chem & Nat Resources Engn Proc Syst Engn Grp Kuantan 26300 Pahang Malaysia Univ Sains Malaysia Seri Ampangan Sch Chem Engn Engn Campus Nibong Tebal 14300 Pulau Pinang Malaysia

Distillation columns are fairly complex multivariable systems and needs to be controlled close to optimum operating conditions because of economic incentives. Nonlinear Model Predictive Control (NMPC) scheme is one of the best options to be explored for proper control of distillation columns. In the present work, a new wavenet based Hammerstein model NMPC has been developed to control distillation column. An experimentally validated equilibrium model was used as plant model in nonlinear system identification and in NMPC. Two multiple-input-single-output (MISO) wavenet based Hammerstein models are developed to model the dynamics of the distillation column. The nonlinear model parameters were estimated using iterative predictionerror minimization method. The Unscented Kalman Filter (UKF) was used to estimate the state variables in NMPC and the NLP problem was solved using sequential quadratic programming (SQP) method. The closed loop control studies have indicated that the performance of developed NMPC scheme was good in controlling the distillation column.

关键词： Distillation column Nonlinear model predictive control sequential quadratic programming Wavenet based Hammerstein model

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RESEARCH ON HULL-FORM OPTIMIZATION OF A PASSENGER SHIP USING HULL-FORM MODIFICATION ALGORITHM WITH GAUSSIAN DISTRIBUTION FUNCTION

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BRODOGRADNJA 2016年第3期67卷 1-16页

作者： Choi, Hee-Jong Yoon, Hyun-Sik Chonnam Natl Univ Dept Naval Architecture & Ocean Engn Yeosu South Korea Pusan Natl Univ Global Core Res Ctr Ships & Offshore Platforms Busan South Korea

The present study proposes an automatic hull form control algorithm to effectively control the hull form of a ship. A Gaussian distribution function is implemented in the proposed algorithm that automatically controls the hull form in conjunction with an optimization algorithm that is executed during the hull form optimization procedure. The hull form optimization algorithm adopts sequential quadratic programming for the optimizer, and the wave-making resistance is used as an objective function and is solved using the potential-based panel method. A high-speed passenger ship is selected as the target ship, and the results of a numerical analysis of the original hull are compared to those of the optimized hull obtained using the hull form optimization in order to verify the effectiveness of the hull-form optimization technique using the proposed automatic hull form control algorithm.

关键词： Hull-form modification Hull-form optimization Gaussian distribution function Passenger ship Potential-based panel method sequential quadratic programming Wave-making resistance

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Mechanical assessment of time optimal robot motion

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COMPUTATIONAL MECHANICS 2004年第2期33卷 121-128页

作者： Giese, G Longman, RW Bock, HG Columbia Univ Dept Mech Engn New York NY 10027 USA Univ Heidelberg Inst Comp Sci D-6900 Heidelberg Germany

The use of time optimal path planning can speed up robots on assembly lines and allow them to run faster, increasing their productivity. This paper seeks to develop a more complete understanding of the nature of time-optimal point-to-point trajectories for polar coordinate robots and intends to show how effective direct numerical methods are in computing optimal control solutions, including the resolution of complicated motor switching structures. In time optimal robot point-to-point motion there is generically one robot axis that has the hardest time reaching its endpoint. And then, to whatever extent other axes have extra freedom, it must be used to help the axis with the hardest task, whenever possible. Such assistance makes use of different mechanical interaction forces and effects. In this paper we examine one basis type of robot, the polar coordinate robot, and analyze all types of forces during optimal motions, in order to develop an understanding of optimal maneuvers.

关键词： optimal robot control polar robot simulation numerical optimization sequential quadratic programming

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AVOIDING THE MARATOS EFFECT BY MEANS OF A NONMONOTONE LINE SEARCH .1. GENERAL CONSTRAINED PROBLEMS

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SIAM JOURNAL ON NUMERICAL ANALYSIS 1991年第4期28卷 1183-1195页

作者： PANIER, ER TITS, AL INST NATL RECH INFORMAT & AUTOMAT PROJECT META2ROCQUENCOURTFRANCE UNIV MARYLAND SYST RES CTRCOLLEGE PKMD 20742 UNIV MARYLAND DEPT ELECT ENGNCOLLEGE PKMD 20742

An essential condition for quasi-Newton optimization methods to converge super-linearly is that a full step of one be taken close to the solution. It is well known that, when dealing with constrained optimization problems, line search schemes ensuring global convergence of such methods may prevent this from occurring (the so-called "Maratos effect"). Two types of techniques have been used to circumvent this difficulty. In the watchdog technique, the full step of one is occasionally accepted even when the line search criterion is violated;subsequent backtracking is used if global convergence appears to be lost. In a "bending" technique proposed by Mayne and Polak [Math programming Stud., 16 (1982), pp. 45-61], backtracking is avoided by performing a search along an arc whose construction requires evaluation of constraint functions at an auxillary point;along this arc, the full step of one is accepted close to a solution. The main idea in the present paper is to combine Mayne and Polak's technique with a nonmonotone line search proposed by Grippo, Lampariello, and Lucidi [SIAM J. Numer. Anal., 23 (1986), pp. 707-716] in the context of unconstrained optimization, in such a way that, after a few iterations, function evaluations are no longer performed at auxiliary points. In a companion paper (part II), it is shown that a refinement of this scheme can be used in the context of recently proposed SQP-based methods generating feasible iterates.

关键词： CONSTRAINED OPTIMIZATION sequential quadratic programming MARATOS EFFECT SUPERLINEAR CONVERGENCE

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A restoration-free filter SQP algorithm for equality constrained optimization

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APPLIED MATHEMATICS AND COMPUTATION 2013年第11期219卷 6016-6029页

作者： Zhu, Xiaojing Pu, Dingguo Tongji Univ Dept Math Shanghai 200092 Peoples R China

In this paper, a trust-region sequential quadratic programming algorithm with a modified filter acceptance mechanism is proposed for nonlinear equality constrained optimization. The most important advantage of the proposed algorithm is its avoidance of any feasibility restoration phase, a necessity in traditional filter methods. We solve quadratic programming subproblems based on the well-known Byrd-Omojokun trust-region method. Inexact solutions to these subproblems are allowed. Under some standard assumptions, global convergence of the proposed algorithm is established. Numerical results show our approach is potentially useful. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Constrained optimization sequential quadratic programming Filter Feasibility restoration

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Toward a Scalable Propeller Performance Map

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JOURNAL OF PROPULSION AND POWER 2015年第4期31卷 1073-1082页

作者： Giannakakis, Panagiotis Laskaridis, Panagiotis Nikolaidis, Theoklis Kalfas, Anestis I. Cranfield Univ Dept Power & Propuls Cranfield MK43 0AL Beds England Aristotle Univ Thessaloniki Dept Mech Engn GR-54124 Thessaloniki Greece

Propeller performance is traditionally represented by a performance map that gives propeller efficiency as a function of the flight Mach number, the power coefficient C-P, and the advance ratio J. This work aims to demonstrate how this map changes when the design C-P and J change and to propose a novel map format that is able to capture the performance of different propeller designs. For this purpose, the propeller performance is simulated using a propeller lifting-line method validated for the SR3 propfan. Subsequently, the propeller model is used within a sequential quadratic programming framework to optimize the blade twist and chord distribution for different sets of design C-P and J. A complete propeller performance map is then generated for each one of the optimized designs. The results demonstrate that all the investigated propellers can be modeled by a common map, which determines separately the ideal efficiency and the viscous losses. The ideal efficiency is given in the traditional format of eta(i) = f (C-P, J), whereas the viscous losses are represented as a function of the relative variables C-P/C-Pdes and J/J(des).

关键词： maps sequential quadratic programming blade twist propeller efficiency iodine Mach number Scalability Advance ratio MAPPING(MATHEMATICAL) Propeller models

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Production optimization using derivative free methods applied to Brugge field case

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2014年第0期114卷 22-37页

作者： Asadollahi, Masoud Naevdal, Geir Dadashpour, Mohsen Kleppe, Jon IRIS N-5008 Bergen Norway Norwegian Univ Sci & Technol NTNU IRIS N-5008 Bergen Norway STATOIL N-7500 Stjordal Norway Norwegian Univ Sci & Technol NTNU IPT N-7031 Trondheim Norway

Recently production optimization has achieved increasing attention in upstream petroleum industry. Here, we evaluate derivative free optimization methods for determination of the optimal production strategy using a numerical reservoir model which was prepared for a comparative study at the SPE Applied Technology Workshop in Brugge, June 2008. The pattern search Hooke-Jeeves, the reflection simplex Nelder-Mead, a new line-search derivative-free and a generalized pattern search methods are applied to the optimization problem. The line-search derivative-free algorithm is developed based on the existing line-search derivative free algorithms hi combination with the Hooke-Jeeves pattern search method. The derivative free optimization results are compared with a gradient based sequential quadratic programming algorithm, but we clearly identify some issues limiting the performance of gradient based algorithms. In real applications our optimization problem is facing very costly function evaluations and at the same time one might have limitations in the computational budget. Therefore we are interested in methods that can improve the objective function with few function evaluations. The line-search derivative-free method performs more efficient and better than the other optimization methods. Ranking among the other four methods is somewhat more difficult, except that the Nelder-Mead method clearly has the slowest performance among these methods. We also observed that optimization with sequential quadratic programming had a high risk of getting trapped in a local optimum, which could be explained by properties of the objective function. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Waterflooding optimization Hooke-Jeeves Nelder-Mead Generalized pattern search sequential quadratic programming Line-search derivative-free Performance ranking method

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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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Optimization of Rotor Tip Cavity Shapes for Mitigating Aerodynamic Tip Leakage Losses

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JOURNAL OF PROPULSION AND POWER 2023年第2期40卷 233-246页

作者： Chen, Yingjie Cai, Le Li, Yiyi Wang, Songtao Damodaran, Murali Cheong Khoo, Boo Harbin Inst Technol Sch Energy Sci & Engn Harbin Peoples R China Natl Univ Singapore Fac Engn Singapore City Singapore

Rotor blade tip leakage loss influences turbine stage efficiency. A parametric optimization method based on five design variables combined with Non-Linear programming by quadratic Lagrangian to optimize the turbine efficiency estimated from computational fluid dynamics analysis has been used to obtain estimates of the optimal cavity depth and split rib location within the tip cavity, which appears to improve the stage efficiency by 1.5%. Besides the design point, the influence of the optimized tip cavity shape impacts the performance of the rotor at different rotational speeds and pressure ratios. In this study, by comparing different tip cavity shapes, it is shown that a dual-cavity shape on the rotor blade tip with a stream-direction split rib can effectively control the air flow bending angle inside the tip clearance and improve the aerodynamic performance. The compressible unsteady Reynolds-averaged Navier-Stokes model is used to verify the adaptability of the optimized tip cavity shape to periodic wake disturbances, and the results demonstrate that the time-averaged estimate of the efficiency can be improved by 1.3% compared to that of the flat rotor tip.

关键词： Unsteady Reynolds Averaged Navier Stokes sequential quadratic programming Aerodynamic Performance High Pressure Turbine Flow Conditions Computational Fluid Dynamics Vortex Structure Entropy Generation Aerodynamic Characteristics Leakage Flow

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