On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.

Exact penalties for variational inequalities with applications to nonlinear complementarity problems

In this paper, we present a new reformulation of the KKT system associated to a variational inequality as a semismooth equation. The reformulation is derived from the concept of differentiable exact penalties for nonlinear programming. The best theoretical results are presented for nonlinear complementarity problems, where simple, verifiable, conditions ensure that the penalty is exact. We close the paper with some preliminary computational tests on the use of a semismooth Newton method to solve the equation derived from the new reformulation. We also compare its performance with the Newton method applied to classical reformulations based on the Fischer-Burmeister function and on the minimum. The new reformulation combines the best features of the classical ones, being as easy to solve as the reformulation that uses the Fischer-Burmeister function while requiring as few Newton steps as the one that is based on the minimum.

Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

This paper addresses the development of several alternative novel hybrid/multi-field variational formulations of the geometrically exact three-dimensional elastostatic beam boundary-value problem. In the framework of the complementary energy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of stresses only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value problem. Both weak and linearized weak forms of the principles are presented. The main features of the principles are highlighted, giving special emphasis to their relationships from both theoretical and computational standpoints. (C) 2010 Elsevier Ltd. All rights reserved.

A hybrid heuristic for the multi-plant capacitated lot sizing problem with setup carry-over

This paper addresses the capacitated lot sizing problem (CLSP) with a single stage composed of multiple plants, items and periods with setup carry-over among the periods. The CLSP is well studied and many heuristics have been proposed to solve it. Nevertheless, few researches explored the multi-plant capacitated lot sizing problem (MPCLSP), which means that few solution methods were proposed to solve it. Furthermore, to our knowledge, no study of the MPCLSP with setup carry-over was found in the literature. This paper presents a mathematical model and a GRASP (Greedy Randomized Adaptive Search Procedure) with path relinking to the MPCLSP with setup carry-over. This solution method is an extension and adaptation of a previously adopted methodology without the setup carry-over. Computational tests showed that the improvement of the setup carry-over is significant in terms of the solution value with a low increase in computational time.

Narrowing socioeconomic inequality in child stunting: the Brazilian experience, 1974–2007

Objective To assess trends in the prevalence and social distribution of child stunting in Brazil to evaluate the effect of income and basic service redistribution policies implemented in that country in the recent past. Methods The prevalence of stunting (height-for-age z score below \22122 using the Child Growth Standards of the World Health Organization) among children aged less than 5 years was estimated from data collected during national household surveys carried out in Brazil in 1974\201375 (n = 34 409), 1989 (n = 7374), 1996 (n = 4149) and 2006\201307 (n = 4414). Absolute and relative socioeconomic inequality in stunting was measured by means of the slope index and the concentration index of inequality, respectively. Findings Over a 33-year period, we documented a steady decline in the national prevalence of stunting from 37.1 per cent to 7.1 per cent. Prevalence dropped from 59.0 per cent to 11.2 per cent in the poorest quintile and from 12.1 per cent to 3.3 per cent among the wealthiest quintile. The decline was particularly steep in the last 10 years of the period (1996 to 2007), when the gaps between poor and wealthy families with children under 5 were also reduced in terms of purchasing power; access to education, health care and water and sanitation services; and reproductive health indicators.Conclusion In Brazil, socioeconomic development coupled with equity-oriented public policies have been accompanied by marked improvements in living conditions and a substantial decline in child undernutrition, as well as a reduction of the gap in nutritional status between children in the highest and lowest socioeconomic quintiles. Future studies will show whether these gains will be maintained under the current global economic crisis

AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

Work disability remains a major problem in rheumatoid arthritis in the 2000s: data from 32 countries in the QUEST-RA Study

Introduction: Work disability is a major consequence of rheumatoid arthritis (RA), associated not only with traditional disease activity variables, but also more significantly with demographic, functional, occupational, and societal variables. Recent reports suggest that the use of biologic agents offers potential for reduced work disability rates, but the conclusions are based on surrogate disease activity measures derived from studies primarily from Western countries. Methods: The Quantitative Standard Monitoring of Patients with RA (QUEST-RA) multinational database of 8,039 patients in 86 sites in 32 countries, 16 with high gross domestic product (GDP) (>24K US dollars (USD) per capita) and 16 low-GDP countries (<11K USD), was analyzed for work and disability status at onset and over the course of RA and clinical status of patients who continued working or had stopped working in high-GDP versus low-GDP countries according to all RA Core Data Set measures. Associations of work disability status with RA Core Data Set variables and indices were analyzed using descriptive statistics and regression analyses. Results: At the time of first symptoms, 86% of men (range 57%-100% among countries) and 64% (19%-87%) of women <65 years were working. More than one third (37%) of these patients reported subsequent work disability because of RA. Among 1,756 patients whose symptoms had begun during the 2000s, the probabilities of continuing to work were 80% (95% confidence interval (CI) 78%-82%) at 2 years and 68% (95% CI 65%-71%) at 5 years, with similar patterns in high-GDP and low-GDP countries. Patients who continued working versus stopped working had significantly better clinical status for all clinical status measures and patient self-report scores, with similar patterns in high-GDP and low-GDP countries. However, patients who had stopped working in high-GDP countries had better clinical status than patients who continued working in low-GDP countries. The most significant identifier of work disability in all subgroups was Health Assessment Questionnaire (HAQ) functional disability score. Conclusions: Work disability rates remain high among people with RA during this millennium. In low-GDP countries, people remain working with high levels of disability and disease activity. Cultural and economic differences between societies affect work disability as an outcome measure for RA.

An analytical approach to the dwarf galaxies cusp problem

Aims. An analytical solution for the discrepancy between observed core-like profiles and predicted cusp profiles in dark matter halos is studied. Methods. We calculate the distribution function for Navarro-Frenk-White halos and extract energy from the distribution, taking into account the effects of baryonic physics processes. Results. We show with a simple argument that we can reproduce the evolution of a cusp to a flat density profile by a decrease of the initial potential energy.

Magnetoconfined levels in a parabolic quantum dot: An analytical solution of a three-dimensional Fock-Darwin problem in a tilted magnetic field

The energy spectrum of an electron confined in a quantum dot (QD) with a three-dimensional anisotropic parabolic potential in a tilted magnetic field was found analytically. The theory describes exactly the mixing of in-plane and out-of-plane motions of an electron caused by a tilted magnetic field, which could be seen, for example, in the level anticrossing. For charged QDs in a tilted magnetic field we predict three strong resonant lines in the far-infrared-absorption spectra.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

An oracle approach for interaction neighborhood estimation in random fields

We consider the problem of interaction neighborhood estimation from the partial observation of a finite number of realizations of a random field. We introduce a model selection rule to choose estimators of conditional probabilities among natural candidates. Our main result is an oracle inequality satisfied by the resulting estimator. We use then this selection rule in a two-step procedure to evaluate the interacting neighborhoods. The selection rule selects a small prior set of possible interacting points and a cutting step remove from this prior set the irrelevant points. We also prove that the Ising models satisfy the assumptions of the main theorems, without restrictions on the temperature, on the structure of the interacting graph or on the range of the interactions. It provides therefore a large class of applications for our results. We give a computationally efficient procedure in these models. We finally show the practical efficiency of our approach in a simulation study.

An alternative to the Pythagorean rule? Reevaluating Problem 1 of cuneiform tablet BM 34 568

The first problem of the Seleucid mathematical cuneiform tablet BM 34 568 calculates the diagonal of a rectangle from its sides without resorting to the Pythagorean rule. For this reason, it has been a source of discussion among specialists ever since its first publication. but so far no consensus in relation to its mathematical meaning has been attained. This paper presents two new interpretations of the scribe`s procedure. based on the assumption that he was able to reduce the problem to a standard Mesopotamian question about reciprocal numbers. These new interpretations are then linked to interpretations of the Old Babylonian tablet Plimpton 322 and to the presence of Pythagorean triples in the contexts of Old Babylonian and Hellenistic mathematics. (C) 2007 Elsevier Inc. All rights reserved.

An algorithm for computerized automatic tuning of power system stabilizers

The main objective of this paper is to relieve the power system engineers from the burden of the complex and time-consuming process of power system stabilizer (PSS) tuning. To achieve this goal, the paper proposes an automatic process for computerized tuning of PSSs, which is based on an iterative process that uses a linear matrix inequality (LMI) solver to find the PSS parameters. It is shown in the paper that PSS tuning can be written as a search problem over a non-convex feasible set. The proposed algorithm solves this feasibility problem using an iterative LMI approach and a suitable initial condition, corresponding to a PSS designed for nominal operating conditions only (which is a quite simple task, since the required phase compensation is uniquely defined). Some knowledge about the PSS tuning is also incorporated in the algorithm through the specification of bounds defining the allowable PSS parameters. The application of the proposed algorithm to a benchmark test system and the nonlinear simulation of the resulting closed-loop models demonstrate the efficiency of this algorithm. (C) 2009 Elsevier Ltd. All rights reserved.

Automatic tuning method for the design of supplementary damping controllers for flexible alternating current transmission system devices

The design of supplementary damping controllers to mitigate the effects of electromechanical oscillations in power systems is a highly complex and time-consuming process, which requires a significant amount of knowledge from the part of the designer. In this study, the authors propose an automatic technique that takes the burden of tuning the controller parameters away from the power engineer and places it on the computer. Unlike other approaches that do the same based on robust control theories or evolutionary computing techniques, our proposed procedure uses an optimisation algorithm that works over a formulation of the classical tuning problem in terms of bilinear matrix inequalities. Using this formulation, it is possible to apply linear matrix inequality solvers to find a solution to the tuning problem via an iterative process, with the advantage that these solvers are widely available and have well-known convergence properties. The proposed algorithm is applied to tune the parameters of supplementary controllers for thyristor controlled series capacitors placed in the New England/New York benchmark test system, aiming at the improvement of the damping factor of inter-area modes, under several different operating conditions. The results of the linear analysis are validated by non-linear simulation and demonstrate the effectiveness of the proposed procedure.