Unconstrained Optimization Model Research Articles

Structure optimization for magnetic equipment of permanent magnet retarder

The main purpose of this research is to perform a magnetic analysis on the magnetic equipment of permanent magnet retarder (PMR) and optimize the structure of magnetic equipment with the commercial FEM software ANSYS and its design optimization module. The FEM model is built as an axisymmetric model according to the characteristics of the structure of magnetic equipment. Using this model, the magnetic field distribution and magnetic force are calculated by ANSYS. The mathematical model of structure optimization is also built. The design variables are structural parameters including the dimensions of permanent magnets and magnetic yoke, and the objective function is the magnetic force. The unconstrained optimization model takes the maximum value of magnetic force as the objective. A first-order optimization method is used to determine the optimum design of this problem. The optimization process works entirely with the ANSYS parametric design language (APDL). The design tools are used to understand design space and the behavior of the dependent variables. It is shown that designing a structure with the ANSYS optimization module and its design tools is an effective means to improve the structure.

Generalized CG-algorithms Based on Rational Sigmoid Model for Unconstrained Optimization

In this paper, we present extension forms of Dai, Yuan (DY) and Fletcher, Reveres (FR) CG algorithms. Our modifications and based on introducing a non-quadratic model (sigmoid function model). These modified algorithms are implemented with Wolfe conditions, where initial step size in each iteration is taken as and the global convergence of the modified DY algorithm is investigated. These modified algorithms are tested on some standard test functions and compared with the original DY and FR algorithms showing considerable improvements over all these comparisons.

Simulated Annealing Optimization of Belt Conveyor Transmission

The belt conveyor is a transporting machine by friction in a continuous manner. The two order helical gearing reducer may be generally used as conveyor transmission, and can reduce speed and increase torque of belt. The objective function may be specified that that total center distance of the reducer incline to minimum, so the optimization model including the property and boundary constraints is created. Then the objective function with penalty terms is converted by penalty strategy with addition type, so as to transform the constrained optimization into the unconstrained optimization model. Considering the problem of low efficiency and local optimum caused by standard optimization methods, the simulated annealing algorithm is adopted to solve the optimization model of Belt Conveyor Transmission, and neural network method is applied to fit relative coefficient, then BFGS Quasi-Newton method is recalled automatically when the setting working precision is achieved again. So that the optimization process is simplified and global optimum is acquired reliably.

Generalized CG-algorithms Based on Rational Sigmoid Model for Unconstrained Optimization

Generalized CG-algorithms Based on Rational Sigmoid Model for Unconstrained Optimization

Research on the Properties of Coaxality Error Objective Function

The unconstrained optimization model applying to radial deviation measurement is established for assessing coaxality errors by the positioned minimum zone method. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory of convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the four-dimensional Euclidean space R4. Therefore, the global minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, as long as it is convergent, can be used to solve the objective function to get the wanted values of coaxality errors by the positioned minimum zone assessment. An example is given to verify the theoretical results presented.

A nonmonotone quasi-Newton trust-region method of conic model for unconstrained optimization

This paper presents a new nonmonotone quasi-Newton trust-region algorithm of the conic model for the solution of unconstrained optimization problems, where the computation of the horizontal vectors is easier and the approximate Hessian matrices can be maintained positive definite. Under reasonable assumptions, the global convergence, the locally linear and superlinear convergence of the proposed algorithm are developed, respectively. It is well known that in applying trust-region algorithms, the basic issue is how to solve the trust-region subproblem efficiently. To deal with the issue, an approximate solution method is developed in this paper. Note that the approximate solution method not only is computationally cheap, but also preserves the strong convergence properties as the exact solution methods. Numerical results are shown for a number of test problems from the literature.

Adjustable entropy function method for support vector machine *

Based on KKT complementary condition in optimization theory, an unconstrained non-differential optimization model for support vector machine is proposed. An adjustable entropy function method is given to deal with the proposed optimization problem and the Newton algorithm is used to figure out the optimal solution. The proposed method can find an optimal solution with a relatively small parameter p, which avoids the numerical overflow in the traditional entropy function methods. It is a new approach to solve support vector machine. The theoretical analysis and experimental results illustrate the feasibility and efficiency of the proposed algorithm.

A trust‐region method with a conic model for unconstrained optimization

AbstractIn this paper, we propose and analyze a new conic trust‐region algorithm for solving the unconstrained optimization problems. A new strategy is proposed to construct the conic model and the relevant conic trust‐region subproblems are solved by an approximate solution method. This approximate solution method is not only easy to implement but also preserves the strong convergence properties of the exact solution methods. Under reasonable conditions, the locally linear and superlinear convergence of the proposed algorithm is established. The numerical experiments show that this algorithm is both feasible and efficient. Copyright © 2008 John Wiley & Sons, Ltd.

A nonmonotone trust-region method of conic model for unconstrained optimization

In this paper, we present a nonmonotone trust-region method of conic model for unconstrained optimization. The new method combines a new trust-region subproblem of conic model proposed in [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231] with a nonmonotone technique for solving unconstrained optimization. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments are conducted to compare this method with the method of [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231].

A Hyperbolic Rational Model for Unconstrained Non-Linear Optimization

A Hyperbolic Rational Model for Unconstrained Non-Linear Optimization

Uniqueness of Solution of Cylindricity Objective Function

Based on the radial deviation measurement, the unconstrained optimization model is established for assessing cylindricity errors by the minimum zone method. The properties of the objective function concerned are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the established cylindricity objective function is a continuous, non-differentiable and convex function defined on the four-dimensional Euclidean space R4. Therefore, the global minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, as long as it is convergent, can be applied to solve the objective function to get the reliable minimum zone cylindricity errors. An example is given to verify the theoretical results presented.

Reactive Tabu Search and Sensor Selection in Active Structural Acoustic Control Problems

A Reactive Tabu Search (RTS) is examined. In addition to a dynamic tabu tenure RTS also detects when the search has entered an unproductive area and restarts RTS based on distinctive features of the unproductive area. We explore the effectiveness of RTS over a static tabu list (of a kind used in many implementations) for a two variable unconstrained discrete optimization model with 9 nearly identical minima and 513 other local minima. One of the key features of this problem is that the two-dimensional domain allows us to provide graphical descriptions of the performance of RTS. We then apply RTS to a sensor selection problem in active structural acoustic control. The objective in this problem is to select a set of 8 sensors out of 462 potential sensor locations so that the noise measured at the 8 chosen sensors is as close as possible to the noise measured at all 462. Computational experiments for data taken from a laboratory test article at NASA Langley Research Center are provided.

Shape analysis of complex profiles

This paper proposes a novel shape representation scheme based on CAD database specifications, and an optimization matching algorithm using the least-squares criterion to determine the pose and scale of objects, and perform out-of-profile inspection. The shapes of interest are two-dimensional (2D) profiles generated by projecting 3D objects onto a 2D inspection plane, the boundaries of which are composed of straight-line segments and circular arcs. This procedure can be applied to automated inspection of machined parts using machine vision systems. The shape model is characterized by four global parameters, based on which all the geometric primitives of the shape are expressed in analytic form. The matching procedure is to find the least-squares error between the true profile of the object and the sensed data, and to satisfy all the geometric constraints among primitives simultaneously. The advantage of the proposed model is that all the primitives of the shape are represented by the same (four) parameters in implicit equations, so that the spatial relationships among them are completely specified by the equations. Based on this representation scheme, the subsequent matching problem is formulated as an unconstrained optimization model, and solved by a gradient-based descent algorithm. In the experimental study, the results generated from the proposed technique are compared with those from two of the most commonly used machine vision approaches: Fourier Descriptors (FDs) and moments. This comparison shows that the method is superior to FDs and moments in error minimization. In addition, a complete procedure for automated design, manufacturing and machine vision inspection of production parts is described.

Interpolation by conic model for unconstrained optimization

This paper describes a method for unconstrained optimization that associates quasi-Newton methods with conic functions. The derivation is based upon the construction of a conic function so that a local nonquadratic model can interpolate two function and one gradient values of the objective function at the last two iterates as a natural extension of existing quasi-Newton methods. The new method is shown to have Q-superlinear rate of convergence under standard assumptions on the objective function, and to decrease the number of line searches for good choice of parameters. Numerical experiments verify that the new method is very successful.