Selective harmonic elimination pulsewidth modulation techniques are some of the control methods used in voltage/current source converters. However, challenges such as the task of finding all the multiple sets of solut...
详细信息
Selective harmonic elimination pulsewidth modulation techniques are some of the control methods used in voltage/current source converters. However, challenges such as the task of finding all the multiple sets of solutions of the switching angles for a given problem may be difficult to deal with. In this paper, a direct minimization of the nonlinear transcendental trigonometric Fourier functions in combination with a random search is discussed. The unipolar (three-level) waveform is used to illustrate the proposed method confirming its ability to find multiple sets of solutions, including a case where 51 angles are sought for single- and three-phase applications. A simple harmonic distortion factor is studied for each set of solutions to assess their performance against the noneliminated harmonics. The results presented both at theoretical and experimental level are in close agreement and confirm the robustness of the proposed approach.
In Ref. 2, four algorithms of dual matrices for function minimization were introduced. These algorithms are characterized by the simultaneous use of two matrices and by the property that the one-dimensional search for...
详细信息
In Ref. 2, four algorithms of dual matrices for function minimization were introduced. These algorithms are characterized by the simultaneous use of two matrices and by the property that the one-dimensional search for the optimal stepsize is not needed for convergence. For a quadratic function, these algorithms lead to the solution in at most n + 1 iterations, where n is the number of variables in the function. Since the one-dimensional search is not needed, the total number of gradient evaluations for convergence is at most n + 2. In this paper, the above-mentioned algorithms are tested numerically by using five nonquadratic functions. In order to investigate the effects of the stepsize on the performances of these algorithms, four schemes for the stepsize factor are employed, two corresponding to small-step processes and two corresponding to large-step processes. The numerical results show that, in spite of the wide range employed in the choice of the stepsize factor, all algorithms exhibit satisfactory convergence properties and compare favorably with the corresponding quadratically convergent algorithms using one-dimensional searches for optimal stepsizes.
In this paper, the method of dual matrices for the minimization of functions is introduced. The method, which is developed on the model of a quadratic function, is characterized by two matrices at each iteration. One ...
详细信息
In this paper, the method of dual matrices for the minimization of functions is introduced. The method, which is developed on the model of a quadratic function, is characterized by two matrices at each iteration. One matrix is such that a linearly independent set of directions can be generated, regardless of the stepsize employed. The other matrix is such that, at the point where the first matrix fails to yield a gradient linearly independent of all the previous gradients, it generates a displacement leading to the minimal point. Thus, the one-dimensional search is bypassed. For a quadratic function, it is proved that the minimal point is obtained in at most n + 1 iterations, where n is the number of variables in the function. Since the one-dimensional search is not needed, the total number of gradient evaluations for convergence is at most n + 2. Three algorithms of the method are presented. A reverse algorithm, which permits the use of only one matrix, is also given. Considerations pertaining to the applications of this method to the minimization of a quadratic function and a nonquadratic function are given. It is believed that, since the one-dimensional search can be bypassed, a considerable amount of computational saving can be achieved.
The effect of nonlinearly scaling the objective function on the variable-metric method is investigated, and Broyden's update is modified so that a property of invariancy to the scaling is satisfied. A new three-pa...
详细信息
The effect of nonlinearly scaling the objective function on the variable-metric method is investigated, and Broyden's update is modified so that a property of invariancy to the scaling is satisfied. A new three-parameter class of updates is generated, and criteria for an optimal choice of the parameters are given. Numerical experiments compare the performance of a number of algorithms of the resulting class.
Abstract: Quasi-Newton methods accelerate the steepest-descent technique for function minimization by using computational history to generate a sequence of approximations to the inverse of the Hessian matrix. ...
详细信息
Abstract: Quasi-Newton methods accelerate the steepest-descent technique for function minimization by using computational history to generate a sequence of approximations to the inverse of the Hessian matrix. This paper presents a class of approximating matrices as a function of a scalar parameter. The problem of optimal conditioning of these matrices under an appropriate norm as a function of the scalar parameter is investigated. A set of computational results verifies the superiority of the new methods arising from conditioning considerations to known methods.
This review will look at function minimization and nonlinear least squares, possibly bounds constrained, using R. These tools derive from the more general context of numerical optimization and mathematical programming...
详细信息
This review will look at function minimization and nonlinear least squares, possibly bounds constrained, using R. These tools derive from the more general context of numerical optimization and mathematical programming. How R developers have tried to make the application of such tools easier for users not familiar with optimization is highlighted. Some limitations of methods and their implementations are mentioned to provide perspective. This article is categorized under: Statistical Models > Nonlinear Models Algorithms and Computational Methods > Numerical Methods
In this paper, a unified method to construct quadratically convergent algorithms for function minimization is described. With this unified method, a generalized algorithm is derived. It is shown that all the existing ...
详细信息
In this paper an attempt is made to provide a unified derivation of various minimization algorithms which use the notion of updating an estimate of the inverse of the Hessian matrix. A new method for updating the esti...
详细信息
The nine quadratically convergent algorithms for function minimization appearing in Ref. 2 are tested through several numerical examples. A quadratic function and four nonquadratic functions are investigated. For the ...
详细信息
暂无评论