Convergence Of Optimization Algorithm Research Articles

Optimal Design of Coupled Inductors of High Power Modular Multilevel Converter Using a Novel Hybrid Model

AbstractDue to the importance of arm inductances in modular multilevel converters (MMC), it is necessary to propose an approach which provide the optimal inductor size considering the technical and manufacturing constraints. The investigations prove that utilizing the coupled inductor enhances converter performance and decreases the required value arm inductance and sub-module capacitor and the final converter volume and mass especially in high power applications. The analytical model of coupled inductors is consisted of circuit, electromagnetic and thermal model which will be combined with MMC circuit model to create the global MMC model. The analytical model of coupled inductor leads to fast convergence of optimization algorithm while it does not provide the accurate results. Another proposed approach is to put a finite element software directly in the optimization loop which intensely increases the optimization time and sometime made it hard to converge. In this paper, a novel hybrid correction loop has been proposed and developed to modify the analytical model parameters while the optimization is running. It effectively increases the results accuracy whereas the optimization does not increase so much. The proposed hybrid correction algorithm was employed in a global optimization loop which tries to minimize the total mass of a high power MMC converter according to the number of series sub-modules per arm. The results show that there is an optimal point which provides the maximum performance dependent to the load specifications, IGBT characteristics, goal function and manufacturing constraints. Also, in this research, the effect of coupled inductors on total converter mass and efficiency was investigated and compared to the state of using uncoupled inductors.

Erratum “A second-order sequential optimality condition associated to the convergence of optimization algorithms”

Erratum “A second-order sequential optimality condition associated to the convergence of optimization algorithms”

A second-order sequential optimality condition associated to the convergence of optimization algorithms

Sequential optimality conditions have recently played an important role on the analysis of the global convergence of optimization algorithms towards first-order stationary points, justifying their stopping criteria. In this paper we introduce a sequential optimality condition that takes into account second-order information and that allows us to improve the global convergence assumptions of several second-order algorithms, which is our main goal. We also present a companion constraint qualification that is less stringent than previous assumptions associated to the convergence of second-order methods, like the joint condition Mangasarian-Fromovitz and Weak Constant Rank. Our condition is also weaker than the Constant Rank Constraint Qualification, which associated it to the convergence of second-order algorithms. This means that we can prove second-order global convergence of well stablished algorithms even when the set of Lagrange multipliers is unbounded, which overcomes a limitation of previous results based on MFCQ. We prove global convergence of well known variations of the augmented Lagrangian and Regularized SQP methods to second-order stationary points under this new weak constraint qualification.

Probabilistic low-rank matrix completion from quantized measurements

We consider the recovery of a low rank real-valued matrix M given a subset of noisy discrete (or quantized) measurements. Such problems arise in several applications such as collaborative filtering, learning and content analytics, and sensor network localization. We consider constrained maximum likelihood estimation of M, under a constraint on the entry-wise infinity-norm of M and an exact rank constraint. We provide upper bounds on the Frobenius norm of matrix estimation error under this model. Previous theoretical investigations have focused on binary (1-bit) quantizers, and been based on convex relaxation of the rank. Compared to the existing binary results, our performance upper bound has faster convergence rate with matrix dimensions when the fraction of revealed observations is fixed. We also propose a globally convergent optimization algorithm based on low rank factorization of M and validate the method on synthetic and real data, with improved performance over previous methods.

Time optimization and state-dependent constraints in the quantum optimal control of molecular orientation

We apply two recent generalizations of monotonically convergent optimization algorithms to the control of molecular orientation by laser fields. We show how to minimize the control duration by a step-wise optimization and maximize the field-free molecular orientation using state-dependent constraints. We discuss the physical relevance of the different results.

Development of CMOS Image Sensor System based on Chaos Particle Swarm

Particle swarm optimization algorithm in solving complex functions, such as slow convergence, accuracy is not high, easily falling into local optimum problem. Based on the chaos optimization is introduced into particle swarm optimization algorithm, given the chaotic particle swarm optimization algorithm. In order to improve the image quality of CMOS image sensor, the image of the main noise source and the distortion of image analysis, this paper present the development of CMOS image sensor system based on chaos particle swarm. Computer CMOS image sensor image quality simulation, the results show that chaotic particle swarm optimization algorithm convergence performance is better than that of particle swarm optimization algorithm.

Comparative study of monotonically convergent optimization algorithms for the control of molecular rotation

We apply two different monotonically convergent optimization algorithms to the control of molecular rotational dynamics by laser pulses. This example represents a quantum control problem where the interaction of the system with the external field is non-linear. We test the validity and accuracy of the two methods on the key control targets of producing molecular orientation and planar delocalization at zero temperature, and maximizing permanent alignment at non-zero temperature.

Development and Tuning of Bacteria Foraging Optimization Algorithm on Cell Formation in Cellular Manufacturing System

Ever since Kevin M. Passino invented the bacteria foraging optimization algorithm, one of the main challenges has been employment of the algorithm to problem areas other than those for which the algorithm was proposed. This research work inquires the applications of designed experiments aided by multiple regression analysis for tuning of this emerging novel optimization algorithm parameters to the cell formation (CF) problem considering operation sequence. In this paper, an attempt is made to tuning chemo tactic and swarming steps parameters meanwhile taking into consideration bacteria foraging optimization algorithm convergence speed and performance. The factorial designed experiment is suggested to create treatments of experiment. The adequacy of the proposed model is analyzed based on some commonly statistical criteria. The results lie in favor of adequacy of the proposed model.

The Extragradient Method for Convex Optimization in the Presence of Computational Errors

In this article, we study convergence of the extragradient method for constrained convex minimization problems in a Hilbert space. Our goal is to obtain an ε-approximate solution of the problem in the presence of computational errors, where ε is a given positive number. Most results known in the literature establish convergence of optimization algorithms, when computational errors are summable. In this article, the convergence of the extragradient method for solving convex minimization problems is established for nonsummable computational errors. We show that the the extragradient method generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant.

THE SUBGRADIENT METHOD FOR SOLVING VARIATIONAL INEQUALITIES WITH COMPUTATIONAL ERRORS IN A HILBERT SPACE

In a Hilbert space, we study the asymptotic behavior of the subgradient method for solving a variational inequality, under the presence of computational errors. Most results known in the literature establish convergence of optimization algorithms, when computational errors are summable. In the present paper, the convergence of the subgradient method to the solution of a variational inequalities is established for nonsummable computational errors. We show that the the subgradient method generates good approximate solutions, if the sequence of computational errors is bounded from above by a constant.

The Extragradient Method for Solving Variational Inequalities in the Presence of Computational Errors

In a Hilbert space, we study the convergence of the subgradient method to a solution of a variational inequality, under the presence of computational errors. Most results known in the literature establish convergence of optimization algorithms, when computational errors are summable. In the present paper, the convergence of the subgradient method for solving variational inequalities is established for nonsummable computational errors. We show that the subgradient method generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant.

Regularizers for structured sparsity

We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in machine learning, statistics and signal processing. It is well known that a linear regression can benefit from knowledge that the underlying regression vector is sparse. The combinatorial problem of selecting the nonzero components of this vector can be “relaxed” by regularizing the squared error with a convex penalty function like the ℓ1 norm. However, in many applications, additional conditions on the structure of the regression vector and its sparsity pattern are available. Incorporating this information into the learning method may lead to a significant decrease of the estimation error. In this paper, we present a family of convex penalty functions, which encode prior knowledge on the structure of the vector formed by the absolute values of the regression coefficients. This family subsumes the ℓ1 norm and is flexible enough to include different models of sparsity patterns, which are of practical and theoretical importance. We establish the basic properties of these penalty functions and discuss some examples where they can be computed explicitly. Moreover, we present a convergent optimization algorithm for solving regularized least squares with these penalty functions. Numerical simulations highlight the benefit of structured sparsity and the advantage offered by our approach over the Lasso method and other related methods.

Robust Optimal Power Flow Solution Using Trust Region and Interior-Point Methods

A globally convergent optimization algorithm for solving large nonlinear optimal power flow (OPF) problems is presented. As power systems become heavily loaded, there is an increasing need for globally convergent OPF algorithms. By global convergence, one means the optimization algorithm being able to converge to an OPF solution, if at least one exists, for any choice of initial point. The globally convergent OPF presented is based on an infinity-norm trust region approach, using interior-point methods to solve the trust region subproblems. The performance of the proposed trust region interior-point OPF algorithm, when applied to the IEEE 30-, 57-, 118-, and 300-bus systems, and to an actual 1211-bus system, is compared with that of two widely used nonlinear interior-point methods, namely, a pure primal-dual and its predictor-corrector variant.

A computational method to estimate the unknown coefficient in a wave equation using boundary measurements

The objective of this article is to develop a computational method, which combines an efficient high-order finite difference method for solving wave equation, auto differentiation tools and globally convergent optimization algorithms to estimate the unknown coefficient in a 1-D wave equation. The forward problem is solved by efficient and higher order finite difference methods while the gradient of the cost functional with respect to the coefficient is calculated by an adjoint code which is generated by an auto differentiation tool, such as Tangent linear and Adjoint Model Compiler. Three numerical examples are conducted to demonstrate the effectiveness, robustness and accuracy of the proposed computational method.

Numerical instabilities and convergence control for convex approximation methods

Convex approximation methods could produce iterative oscillation of solutions for solving some problems in structural optimization. This paper firstly analyzes the reason for numerical instabilities of iterative oscillation of the popular convex approximation methods, such as CONLIN (Convex Linearization), MMA (Method of Moving Asymptotes), GCMMA (Global Convergence of MMA) and SQP (Sequential Quadratic Programming), from the perspective of chaotic dynamics of a discrete dynamical system. Then, the usual four methods to improve the convergence of optimization algorithms are reviewed, namely, the relaxation method, move limits, moving asymptotes and trust region management. Furthermore, the stability transformation method (STM) based on the chaos control principle is suggested, which is a general, simple and effective method for convergence control of iterative algorithms. Moreover, the relationships among the former four methods and STM are exposed. The connection between convergence control of iterative algorithms and chaotic dynamics is established. Finally, the STM is applied to the convergence control of convex approximation methods for optimizing several highly nonlinear examples. Numerical tests of convergence comparison and control of convex approximation methods illustrate that STM can stabilize the oscillating solutions for CONLIN and accelerate the slow convergence for MMA and SQP.

A hybrid algorithm for solving the EEG inverse problem from spatio-temporal EEG data

Epilepsy is a neurological disorder caused by intense electrical activity in the brain. The electrical activity, which can be modelled through the superposition of several electrical dipoles, can be determined in a non-invasive way by analysing the electro-encephalogram. This source localization requires the solution of an inverse problem. Locally convergent optimization algorithms may be trapped in local solutions and when using global optimization techniques, the computational effort can become expensive. Fast recovery of the electrical sources becomes difficult that way. Therefore, there is a need to solve the inverse problem in an accurate and fast way. This paper performs the localization of multiple dipoles using a global-local hybrid algorithm. Global convergence is guaranteed by using space mapping techniques and independent component analysis in a computationally efficient way. The accuracy is locally obtained by using the Recursively Applied and Projected-MUltiple Signal Classification (RAP-MUSIC) algorithm. When using this hybrid algorithm, a four times faster solution is obtained.

Globally Convergent Optimization Algorithms on Riemannian Manifolds: Uniform Framework for Unconstrained and Constrained Optimization

This paper proposes several globally convergent geometric optimization algorithms on Riemannian manifolds, which extend some existing geometric optimization techniques. Since any set of smooth constraints in the Euclidean space Rn (corresponding to constrained optimization) and the Rn space itself (corresponding to unconstrained optimization) are both special Riemannian manifolds, and since these algorithms are developed on general Riemannian manifolds, the techniques discussed in this paper provide a uniform framework for constrained and unconstrained optimization problems. Unlike some earlier works, the new algorithms have less restrictions in both convergence results and in practice. For example, global minimization in the one-dimensional search is not required. All the algorithms addressed in this paper are globally convergent. For some special Riemannian manifold other than Rn, the new algorithms are very efficient. Convergence rates are obtained. Applications are discussed.

Simultaneous estimation of temperature-dependent thermal conductivity and heat capacity based on modified genetic algorithm

An inverse heat conduction analysis is presented to simultaneously estimate the temperature-dependent thermal conductivity and heat capacity based on a modified elitist genetic algorithm (MEGA). In this study, MEGA is used to minimize a least squares objective function containing estimated and simulated (filtered) temperatures. The estimated temperatures are obtained from the direct numerical solution (finite differences method, or FDM) of the finite one-dimensional conductive model by using an estimate for the unknown temperature-dependent thermophysical properties (TDTPs). The accuracy of the MEGA is assessed by comparing the estimated and the preselected TDTPs. The results of the MEGA are used as the starting point for a locally convergent optimization algorithm, i.e., the Levenberg–Marquardt (L–M) method. It is shown in this work that hybridization of the MEGA with the L–M method can lead to accurate estimates. From the results, it is found that the RMS error between estimated and simulated temperatures is very small irrespective of whether measurement errors are included or excluded. In addition to estimation of the TDTPs, sensitivity analysis is performed to investigate the effects of heating duration. Also, it is found that the results of the MEGA are highly satisfactory with only single-sensor measurements on the heated surface.

An experimental study of projective structure from motion

We describe an essentially algorithm-independent experimental comparison of projective versus Euclidean reconstruction. The Euclidean approach is as accurate as the projective one, even with significant calibration error and for the pure projective structure. Projective optimization has less of a local-minima problem than its Euclidean equivalent. We describe techniques that enhance the convergence of optimization algorithms.

Concavity of queueing systems with NBU service times

This paper establishes structural properties for the throughput of a large class of queueing networks with i.i.d. new-better-than-used service times. The main result obtained in this paper is applied to a wide range of networks, including tandems, cycles and fork-join networks with general blocking and starvation (as well as certain networks with splitting and merging of traffic streams), to deduce the concavity of their throughput as a function of system parameters, such as buffer and initial job configurations, and blocking and starvation parameters. These results have important implications for the optimal design and control of such queueing networks by providing exact solutions, reducing the search space over which optimization need be performed, or establishing the convergence of optimization algorithms. In order to obtain results for such disparate networks in a unified manner, we introduce the framework of constrained discrete event systems (CDES), which enables us to characterize any permutable and non-interruptive queueing network through its constraint set. The main result of this paper establishes comparison properties of the event occurrence processes of CDES as a function of the constraint sets, which are then translated into the above-mentioned concavity of the throughput as a function of system parameters in the context of queueing networks.