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 reprojecti...
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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.
作者:
Youn, BDChoi, KKUniv 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 ...
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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.
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. Perform...
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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.
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 pr...
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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.
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 v...
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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.
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 sh...
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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.
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 l...
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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 quadraticprogramming 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.
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...
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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.
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 me...
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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.
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 weak...
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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.
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