Perturbed Proximal Point Algorithm with Nonquadratic Kernel

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of these extensions by taking simultaneously into account a pseudo-metric as regularization and a perturbation in an inexact version of the algorithm.

Interior point algorithm for linear programming used in transmission network synthesis

This article presents a well-known interior point method (IPM) used to solve problems of linear programming that appear as sub-problems in the solution of the long-term transmission network expansion planning problem. The linear programming problem appears when the transportation model is used, and when there is the intention to solve the planning problem using a constructive heuristic algorithm (CHA), ora branch-and-bound algorithm. This paper shows the application of the IPM in a CHA. A good performance of the IPM was obtained, and then it can be used as tool inside algorithm, used to solve the planning problem. Illustrative tests are shown, using electrical systems known in the specialized literature. (C) 2005 Elsevier B.V. All rights reserved.

Convergence analysis and validation of low cost distance metrics for computational cost reduction of the Iterative Closest Point algorithm

The Iterative Closest Point algorithm (ICP) is commonly used in engineering applications to solve the rigid registration problem of partially overlapped point sets which are pre-aligned with a coarse estimate of their relative positions. This iterative algorithm is applied in many areas such as the medicine for volumetric reconstruction of tomography data, in robotics to reconstruct surfaces or scenes using range sensor information, in industrial systems for quality control of manufactured objects or even in biology to study the structure and folding of proteins. One of the algorithm’s main problems is its high computational complexity (quadratic in the number of points with the non-optimized original variant) in a context where high density point sets, acquired by high resolution scanners, are processed. Many variants have been proposed in the literature whose goal is the performance improvement either by reducing the number of points or the required iterations or even enhancing the complexity of the most expensive phase: the closest neighbor search. In spite of decreasing its complexity, some of the variants tend to have a negative impact on the final registration precision or the convergence domain thus limiting the possible application scenarios. The goal of this work is the improvement of the algorithm’s computational cost so that a wider range of computationally demanding problems from among the ones described before can be addressed. For that purpose, an experimental and mathematical convergence analysis and validation of point-to-point distance metrics has been performed taking into account those distances with lower computational cost than the Euclidean one, which is used as the de facto standard for the algorithm’s implementations in the literature. In that analysis, the functioning of the algorithm in diverse topological spaces, characterized by different metrics, has been studied to check the convergence, efficacy and cost of the method in order to determine the one which offers the best results. Given that the distance calculation represents a significant part of the whole set of computations performed by the algorithm, it is expected that any reduction of that operation affects significantly and positively the overall performance of the method. As a result, a performance improvement has been achieved by the application of those reduced cost metrics whose quality in terms of convergence and error has been analyzed and validated experimentally as comparable with respect to the Euclidean distance using a heterogeneous set of objects, scenarios and initial situations.

The Perturbed Generalized Tikhonov's Algorithm

We work on the research of a zero of a maximal monotone operator on a real Hilbert space. Following the recent progress made in the context of the proximal point algorithm devoted to this problem, we introduce simultaneously a variable metric and a kind of relaxation in the perturbed Tikhonov’s algorithm studied by P. Tossings. So, we are led to work in the context of the variational convergence theory.

A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function

2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.

Proximal methods for nonlinear programming: double regularization and inexact subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.

Fixed-point DSP implementation of nonlinear H(infinity) controller for large gap electromagnetic suspension system

Electromagnetic suspension systems are inherently nonlinear and often face hardware limitation when digitally controlled. The main contributions of this paper are: the design of a nonlinear H(infinity) controller. including dynamic weighting functions, applied to a large gap electromagnetic suspension system and the presentation of a procedure to implement this controller on a fixed-point DSP, through a methodology able to translate a floating-point algorithm into a fixed-point algorithm by using l(infinity) norm minimization due to conversion error. Experimental results are also presented, in which the performance of the nonlinear controller is evaluated specifically in the initial suspension phase. (C) 2009 Elsevier Ltd. All rights reserved.

Stereo-Based Head Pose Tracking Using Iterative Closest Point and Normal Flow Constraint

In this text, we present two stereo-based head tracking techniques along with a fast 3D model acquisition system. The first tracking technique is a robust implementation of stereo-based head tracking designed for interactive environments with uncontrolled lighting. We integrate fast face detection and drift reduction algorithms with a gradient-based stereo rigid motion tracking technique. Our system can automatically segment and track a user's head under large rotation and illumination variations. Precision and usability of this approach are compared with previous tracking methods for cursor control and target selection in both desktop and interactive room environments. The second tracking technique is designed to improve the robustness of head pose tracking for fast movements. Our iterative hybrid tracker combines constraints from the ICP (Iterative Closest Point) algorithm and normal flow constraint. This new technique is more precise for small movements and noisy depth than ICP alone, and more robust for large movements than the normal flow constraint alone. We present experiments which test the accuracy of our approach on sequences of real and synthetic stereo images. The 3D model acquisition system we present quickly aligns intensity and depth images, and reconstructs a textured 3D mesh. 3D views are registered with shape alignment based on our iterative hybrid tracker. We reconstruct the 3D model using a new Cubic Ray Projection merging algorithm which takes advantage of a novel data structure: the linked voxel space. We present experiments to test the accuracy of our approach on 3D face modelling using real-time stereo images.

Reactive power dispatch and planning using a non-linear branch-and-bound algorithm

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Inverse aerodynamic design applications using the MGM hybrid formulation

The well-known modified Garabedian-Mcfadden (MGM) method is an attractive alternative for aerodynamic inverse design, for its simplicity and effectiveness (P. Garabedian and G. Mcfadden, Design of supercritical swept wings, AIAA J. 20(3) (1982), 289-291; J.B. Malone, J. Vadyak, and L.N. Sankar, Inverse aerodynamic design method for aircraft components, J. Aircraft 24(2) (1987), 8-9; Santos, A hybrid optimization method for aerodynamic design of lifting surfaces, PhD Thesis, Georgia Institute of Technology, 1993). Owing to these characteristics, the method has been the subject of several authors over the years (G.S. Dulikravich and D.P. Baker, Aerodynamic shape inverse design using a Fourier series method, in AIAA paper 99-0185, AIAA Aerospace Sciences Meeting, Reno, NV, January 1999; D.H. Silva and L.N. Sankar, An inverse method for the design of transonic wings, in 1992 Aerospace Design Conference, No. 92-1025 in proceedings, AIAA, Irvine, CA, February 1992, 1-11; W. Bartelheimer, An Improved Integral Equation Method for the Design of Transonic Airfoils and Wings, AIAA Inc., 1995). More recently, a hybrid formulation and a multi-point algorithm were developed on the basis of the original MGM. This article discusses applications of those latest developments for airfoil and wing design. The test cases focus on wing-body aerodynamic interference and shock wave removal applications. The DLR-F6 geometry is picked as the baseline for the analysis.

Dynamic higher order expectations

In models where privately informed agents interact, agents may need to formhigher order expectations, i.e. expectations of other agents' expectations. This paper develops a tractable framework for solving and analyzing linear dynamic rational expectationsmodels in which privately informed agents form higher order expectations. The frameworkis used to demonstrate that the well-known problem of the infinite regress of expectationsidentified by Townsend (1983) can be approximated to an arbitrary accuracy with a finitedimensional representation under quite general conditions. The paper is constructive andpresents a fixed point algorithm for finding an accurate solution and provides weak conditions that ensure that a fixed point exists. To help intuition, Singleton's (1987) asset pricingmodel with disparately informed traders is used as a vehicle for the paper.

A Practical Micro Mechanical Model Based Local Approach Methodology for the Analysis of Ductile Fracture of Welded T-Joints

This thesis concentrates on developing a practical local approach methodology based on micro mechanical models for the analysis of ductile fracture of welded joints. Two major problems involved in the local approach, namely the dilational constitutive relation reflecting the softening behaviour of material, and the failure criterion associated with the constitutive equation, have been studied in detail. Firstly, considerable efforts were made on the numerical integration and computer implementation for the non trivial dilational Gurson Tvergaard model. Considering the weaknesses of the widely used Euler forward integration algorithms, a family of generalized mid point algorithms is proposed for the Gurson Tvergaard model. Correspondingly, based on the decomposition of stresses into hydrostatic and deviatoric parts, an explicit seven parameter expression for the consistent tangent moduli of the algorithms is presented. This explicit formula avoids any matrix inversion during numerical iteration and thus greatly facilitates the computer implementation of the algorithms and increase the efficiency of the code. The accuracy of the proposed algorithms and other conventional algorithms has been assessed in a systematic manner in order to highlight the best algorithm for this study. The accurate and efficient performance of present finite element implementation of the proposed algorithms has been demonstrated by various numerical examples. It has been found that the true mid point algorithm (a = 0.5) is the most accurate one when the deviatoric strain increment is radial to the yield surface and it is very important to use the consistent tangent moduli in the Newton iteration procedure. Secondly, an assessment of the consistency of current local failure criteria for ductile fracture, the critical void growth criterion, the constant critical void volume fraction criterion and Thomason's plastic limit load failure criterion, has been made. Significant differences in the predictions of ductility by the three criteria were found. By assuming the void grows spherically and using the void volume fraction from the Gurson Tvergaard model to calculate the current void matrix geometry, Thomason's failure criterion has been modified and a new failure criterion for the Gurson Tvergaard model is presented. Comparison with Koplik and Needleman's finite element results shows that the new failure criterion is fairly accurate indeed. A novel feature of the new failure criterion is that a mechanism for void coalescence is incorporated into the constitutive model. Hence the material failure is a natural result of the development of macroscopic plastic flow and the microscopic internal necking mechanism. By the new failure criterion, the critical void volume fraction is not a material constant and the initial void volume fraction and/or void nucleation parameters essentially control the material failure. This feature is very desirable and makes the numerical calibration of void nucleation parameters(s) possible and physically sound. Thirdly, a local approach methodology based on the above two major contributions has been built up in ABAQUS via the user material subroutine UMAT and applied to welded T joints. By using the void nucleation parameters calibrated from simple smooth and notched specimens, it was found that the fracture behaviour of the welded T joints can be well predicted using present methodology. This application has shown how the damage parameters of both base material and heat affected zone (HAZ) material can be obtained in a step by step manner and how useful and capable the local approach methodology is in the analysis of fracture behaviour and crack development as well as structural integrity assessment of practical problems where non homogeneous materials are involved. Finally, a procedure for the possible engineering application of the present methodology is suggested and discussed.

Construction d'un Atlas 3D numérique de la cornée humaine par recalage d'images

Nous proposons de construire un atlas numérique 3D contenant les caractéristiques moyennes et les variabilités de la morphologie d’un organe. Nos travaux seront appliqués particulièrement à la construction d'un atlas numérique 3D de la totalité de la cornée humaine incluant la surface antérieure et postérieure à partir des cartes topographiques fournies par le topographe Orbscan II. Nous procédons tout d'abord par normalisation de toute une population de cornées. Dans cette étape, nous nous sommes basés sur l'algorithme de recalage ICP (iterative closest point) pour aligner simultanément les surfaces antérieures et postérieures d'une population de cornée vers les surfaces antérieure et postérieure d'une cornée de référence. En effet, nous avons élaboré une variante de l'algorithme ICP adapté aux images (cartes) de cornées qui tient compte de changement d'échelle pendant le recalage et qui se base sur la recherche par voisinage via la distance euclidienne pour établir la correspondance entre les points. Après, nous avons procédé pour la construction de l'atlas cornéen par le calcul des moyennes des élévations de surfaces antérieures et postérieures recalées et leurs écarts-types associés. Une population de 100 cornées saines a été utilisée pour construire l'atlas cornéen normal. Pour visualiser l’atlas, on a eu recours à des cartes topographiques couleurs similairement à ce qu’offrent déjà les systèmes topographiques actuels. Enfin, des observations ont été réalisées sur l'atlas cornéen reflétant sa précision et permettant de développer une meilleure connaissance de l’anatomie cornéenne.

Multi-areas optimal reactive power flow

This paper describes a method for the decentralized solution of the optimal reactive power flow (ORPF) problem in interconnected power systems. The ORPF model is solved in a decentralized framework, consisting of regions, where the transmission system operator in each area operates its system independently of the other areas, obtaining an optimal coordinated but decentralized solution. The proposed scheme is based on an augmented Lagrangian approach using the auxiliary problem principle (APP). An implementation of an interior point method is described to solve the decoupled problem in each area. The described method is successfully implemented and tested using the IEEE two area RTS 96 test system. Numerical results comparing the solutions obtained by the traditional and the proposed decentralized methods are presented for validation. ©2008 IEEE.