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quadratic surface reconstruction from multiple views using SQP

IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2004年第1期E87D卷 215-223页

作者： Gong, RB Xu, G Ritsumeikan Univ Dept Comp Sci Kusatsu 5258577 Japan

We propose using SQP (sequential quadratic programming) to directly recover 3D quadratic surface parameters from multiple views. A surface equation is used as a constraint. In addition to the sum of squared reprojection errors defined in the traditional bundle adjustment, a Lagrangian term is added to force recovered points to satisfy the constraint. The minimization is realized by SQP. Our algorithm has three advantages. First, given corresponding features in multiple views, the SQP implementation can directly recover the quadratic surface parameters optimally instead of a collection of isolated 3D points coordinates. Second, the specified constraints are strictly satisfied and the camera parameters and 3D coordinates of points can be determined more accurately than that by unconstrained methods. Third, the recovered quadratic surface model can be represented by a much smaller number of parameters instead of point clouds and triangular patches. Experiments with both synthetic and real images show the power of this approach.

关键词： quadratic surface reconstruction constrained minimization sequential quadratic programming bundle adjustment error analysis

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Selecting probabilistic approaches for reliability-based design optimization

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AIAA JOURNAL 2004年第1期42卷 124-131页

作者： Youn, BD Choi, KK Univ Iowa Ctr Comp Aided Design Coll Engn Iowa City IA 52241 USA Univ Iowa Dept Mech Engn Coll Engn Iowa City IA 52241 USA

During the past decade, numerous endeavors have been made to develop effective reliability-based design optimization (RBDO) methods. Because the evaluation of probabilistic constraints defined in the RBDO formulation is the most difficult part to deal with, a number of different probabilistic design approaches have been proposed to evaluate probabilistic constraints in RBDO In the first approach, statistical moments are approximated to evaluate the probabilistic constraint. Thus, this is referred to as the approximate moment approach (AMA). The second approach, called the reliability index approach (RIA), describes the probabilistic constraint as a reliability index. Last, the performance measure approach (PMA) was proposed by converting the probability measure to a performance measure. A guide for selecting an appropriate method in RBDO is provided by comparing probabilistic design approaches for RBDO from the perspective of various numerical considerations. It has been found in the literature that PMA is more efficient and stable than RIA in the RBDO process. It is found that PMA is accurate enough and stable at an allowable efficiency, whereas AMA has some difficulties in RBDO process such as a second-order design sensitivity required for design optimization, an inaccuracy to measure a probability of failure, and numerical instability due to its inaccuracy. Consequently, PMA has several major advantages over AMA, in terms of numerical accuracy, simplicity, and stability. Some numerical examples are shown to demonstrate several numerical observations on the three different RBDO approaches.

关键词： Cumulative Distribution Function sequential quadratic programming Sensitivity Analysis Monte Carlo Simulation Iterative Algorithm Crashworthiness Design of Experiments Search Algorithm Structural Modeling Computing Power

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Optimization of pass schedules for a tandem cold mill

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TETSU TO HAGANE-JOURNAL OF THE IRON AND STEEL INSTITUTE OF JAPAN 2004年第11期90卷 953-957页

作者： Murakami, AA Nakayama, M Okamoto, M Abiko, Y Sano, K Tsuchihashi, T Kobe Steel Ltd Tech Dev Grp Nishi Ku Kobe Hyogo 6512271 Japan Kobe Steel Ltd Kakogawa Works Kobe Hyogo Japan

Pass schedules for a tandem cold mill affect the productivity and quality of rolled strips. This paper describes optimization of pass schedules, which are optimized via sequential quadratic programming method. Performance functions and constraint conditions are chosen to achieve desired rolling conditions such as rolling forces, motor electric currents and reductions in thickness. Consequently, strips with small gage tolerance can be produced at higher productivity. The newly optimized pass schedules are applied to a 5-stand tandem cold mill. The results showed 3% decrease in off-gage length and 0.4% increase in productivity.

关键词： tandem cold mill pass schedule optimization sequential quadratic programming

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3D structure from a single calibrated view using distance constraints

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2004年第6期E87D卷 1527-1536页

作者： Gong, RB Xu, G Ritsumeikan Univ Kusatsu 5258577 Japan

We propose a new method to recover scene points from a single calibrated view using a subset of distances among the points. This paper first introduces the problem and its relationship with the perspective 17 point problem. Then the number of distances required to uniquely recover scene points are explored. The result is then developed into a practical vision algorithm to calculate the initial points' coordinates using distance constraints. Finally SQP (sequential quadratic programming) is used to optimize the initial estimations. It can minimize a cost function defined as the sum of squared reprojection errors while keeping the specified distance constraints strictly satisfied. Both simulation data and real scene images have been used to test the proposed method, and good results have been obtained.

关键词： perspective n point problem single view reconstruction sensitivity analysis sequential quadratic programming

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Structural design optimization of shallow frame structures undergoing large deflections

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AIAA JOURNAL 2004年第12期42卷 2592-2599页

作者： Sedaghati, R Suleman, A Concordia Univ Dept Mech & Ind Engn Montreal PQ H3G 1M8 Canada Univ Victoria Dept Mech Engn Victoria BC V8W 3P6 Canada

An optimization algorithm for structural design against instability is developed for shallow beam structures undergoing large deflections. The algorithm is based on the maximization of the limit load under specified volume constraint. The analysis for obtaining the limit load involves coupling of axial and bending deformations and is based on the nonlinear finite element analysis using the displacement control technique. The optimization is carried out using both the sequential-quadratic-programming (SQP) and optimality-criterion (OC) techniques, and the results are compared. For the SQP technique, the sensitivity derivatives of the critical load factor are calculated using the adjoint method based on the information obtained from the nonlinear buckling analysis. A shallow plane arch illustrates the structural design optimization methodology, and the results are compared with those in the literature. It is shown that a design based on the generalized eigenvalue problem (linear buckling) gives an optimum limit load less than the initial limit load, whereas the optimization using the nonlinear buckling analysis obtains a larger value for the optimum limit load compared to the initial limit load. It has also been demonstrated that the optimum results obtained using OC technique are in good agreement with those obtained through SQP technique. However, the computational time for the OC is significantly lower than that of SQP, which requires search techniques and sensitivity of the limit load for its successful completion and termination.

关键词： Structural Optimization Finite Element Analysis sequential quadratic programming Buckling Analysis Critical Loading Beam (Structures) Lagrange Multipliers Energy Density Young's Modulus Composite Structures

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sequential quadratic programming for large-scale nonlinear optimization

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2000年第1-2期124卷 123-137页

作者： Boggs, PT Tolle, JW Sandia Natl Labs Comp Sci & Math Res Dept Livermore CA 94550 USA Univ N Carolina Dept Operat Res & Math Chapel Hill NC 27514 USA

The sequential quadratic programming (SQP) algorithm has been one of the most successful general methods for solving nonlinear constrained optimization problems. We provide an introduction to the general method and show its relationship to recent developments in interior-point approaches, emphasizing large-scale aspects. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： sequential quadratic programming nonlinear optimization Newton methods interior-point methods local trust-region methods convergence global convergence

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An efficient interior point method for sequential quadratic programming based optimal power flow

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IEEE TRANSACTIONS ON POWER SYSTEMS 2000年第4期15卷 1179-1183页

作者： Nejdawi, IM Clements, KA Davis, PW Worcester Polytech Inst Worcester MA 01609 USA

This paper presents a new sequential quadratic programming algorithm for solving the optimal power flow problem. The algorithm is structured with an outer linearization loop and an inner optimization loop. The inner loop solves a relaxed reduced quadratic programming problem. Because constraint relaxation keeps the inner loop problem of small dimension, the algorithm is quite efficient. Its outer loop iteration counts are comparable to Newton power flow, and the inner loops are efficient interior point iterations. Several IEEE test systems were run. The results indicate that both outer and inner loop iteration counts do not vary greatly with problem size.

关键词： interior-point methods nonlinear programming optimal power flow sequential quadratic programming

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New Stochastic algorithm for design optimization

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AIAA JOURNAL 2003年第9期41卷 1808-1818页

作者： de Sousa, FL Ramos, FM Paglione, P Girardi, RM Inst Nacl Pesquisas Espaciais Div Mecan Espacial & Control BR-12227010 Sao Jose Dos Campos Brazil Inst Nacl Pesquisas Espaciais Lab Assoc Comp & Matemat Aplicada BR-12227010 Sao Jose Dos Campos Brazil Inst Tecnol Aeronaut Div Engn Aeronaut BR-12228900 Sao Jose Dos Campos Brazil

A new stochastic algorithm for design optimization is introduced. Called generalized extremal optimization (GEO), it is intended to be used in complex optimization problems where traditional gradient-based methods may become inefficient, such as when applied to a nonconvex or disjoint design space, or when there are different kinds of design variables in it. The algorithm is easy to implement, does not make use of derivatives, and can be applied to unconstrained or constrained problems, and nonconvex or disjoint design spaces, in the presence of any combination of continuous, discrete, or integer variables. It is a global search metaheuristic, as are genetic algorithms (GAs) and simulated annealing (SA), but with the a priori advantage of having only one free parameter to adjust. The algorithm is presented in two implementations and its performance is assessed on a set of test functions. A simple application to the design of a glider airfoil is also presented. It is shown that the GEO algorithm is competitive in performance with the GA and SA and is an attractive tool to be used on applications in the aerospace field.

关键词： NACA Airfoil Annealing Genetic Algorithm sequential quadratic programming Probability Distribution Aerodynamic Performance Boundary Layer Separation Evolutionary Algorithm Stagnation Point Stochastic Optimization

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Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function

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MATHEMATICAL programming 2003年第1期95卷 103-135页

作者： Ulbrich, M Ulbrich, S Tech Univ Munich Zentrum Math D-80290 Munich Germany

We propose and analyze a class of penalty-function-free nonmonotone trust-region methods for nonlinear equality constrained optimization problems. The algorithmic framework yields global convergence without using a merit function and allows nonmonotonicity independently for both, the constraint violation and the value of the Lagrangian function. Similar to the Byrd-Omojokun class of algorithms, each step is composed of a quasi-normal and a tangential step. Both steps are required to satisfy a decrease condition for their respective trust-region subproblems. The proposed mechanism for accepting steps combines nonmonotone decrease conditions on the constraint violation and/or the Lagrangian function, which leads to a flexibility and acceptance behavior comparable to filter-based methods. We establish the global convergence of the method. Furthermore, transition to quadratic local convergence is proved. Numerical tests are presented that confirm the robustness and efficiency of the approach.

关键词： nonmonotone trust-region methods sequential quadratic programming penalty function global convergence equality constraints local convergence large-scale optimization

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Constraint identification and algorithm stabilization for degenerate nonlinear programs

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MATHEMATICAL programming 2003年第1期95卷 137-160页

作者： Wright, SJ Univ Wisconsin Dept Comp Sci Madison WI 53706 USA

In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly active constraints. We show that this information can be used to modify the sequential quadratic programming algorithm so that it exhibits superlinear convergence to the solution under assumptions weaker than those made in previous analyses.

关键词： nonlinear programming problems degeneracy active constraint identification sequential quadratic programming

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