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.

Using sentinels to detect intersections of convex and nonconvex polygons

We describe finite sets of points, called sentinels, which allow us to decide if isometric copies of polygons, convex or not, intersect. As an example of the applicability of the concept of sentinel, we explain how they can be used to formulate an algorithm based on the optimization of differentiable models to pack polygons in convex sets. Mathematical subject classification: 90C53, 65K05.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Recycling Krylov subspaces for efficient large-scale electrical impedance tomography

Electrical impedance tomography (EIT) captures images of internal features of a body. Electrodes are attached to the boundary of the body, low intensity alternating currents are applied, and the resulting electric potentials are measured. Then, based on the measurements, an estimation algorithm obtains the three-dimensional internal admittivity distribution that corresponds to the image. One of the main goals of medical EIT is to achieve high resolution and an accurate result at low computational cost. However, when the finite element method (FEM) is employed and the corresponding mesh is refined to increase resolution and accuracy, the computational cost increases substantially, especially in the estimation of absolute admittivity distributions. Therefore, we consider in this work a fast iterative solver for the forward problem, which was previously reported in the context of structural optimization. We propose several improvements to this solver to increase its performance in the EIT context. The solver is based on the recycling of approximate invariant subspaces, and it is applied to reduce the EIT computation time for a constant and high resolution finite element mesh. In addition, we consider a powerful preconditioner and provide a detailed pseudocode for the improved iterative solver. The numerical results show the effectiveness of our approach: the proposed algorithm is faster than the preconditioned conjugate gradient (CG) algorithm. The results also show that even on a standard PC without parallelization, a high mesh resolution (more than 150,000 degrees of freedom) can be used for image estimation at a relatively low computational cost. (C) 2010 Elsevier B.V. All rights reserved.

Assembling a consistent set of sentences in relational probabilistic logic with stochastic independence

We examine the representation of judgements of stochastic independence in probabilistic logics. We focus on a relational logic where (i) judgements of stochastic independence are encoded by directed acyclic graphs, and (ii) probabilistic assessments are flexible in the sense that they are not required to specify a single probability measure. We discuss issues of knowledge representation and inference that arise from our particular combination of graphs, stochastic independence, logical formulas and probabilistic assessments. (C) 2007 Elsevier B.V. All rights reserved.

Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.

ECONOMICAL OCCUPATION OF AGRICULTURAL AREA OF PIRACICABA (SAO PAULO STATE, BRAZIL), INCLUDING RISK THROUGH LINEAR PROGRAMMING

The economic occupation of an area of 500 ha for Piracicaba was studied with the irrigated cultures of maize, tomato, sugarcane and beans, having used models of deterministic linear programming and linear programming including risk for the Target-Motad model, where two situations had been analyzed. In the deterministic model the area was the restrictive factor and the water was not restrictive for none of the tested situations. For the first situation the gotten maximum income was of R$ 1,883,372.87 and for the second situation it was of R$ 1,821,772.40. In the model including risk a producer that accepts risk can in the first situation get the maximum income of R$ 1,883,372. 87 with a minimum risk of R$ 350 year(-1), and in the second situation R$ 1,821,772.40 with a minimum risk of R$ 40 year(-1). Already a producer averse to the risk can get in the first situation a maximum income of R$ 1,775,974.81 with null risk and for the second situation R$ 1.707.706, 26 with null risk, both without water restriction. These results stand out the importance of the inclusion of the risk in supplying alternative occupations to the producer, allowing to a producer taking of decision considered the risk aversion and the pretension of income.

Stability property of matchings is a natural solution concept in coalitional market games

Stability of matchings was proved to be a new cooperative equilibrium concept in Sotomayor (Dynamics and equilibrium: essays in honor to D. Gale, 1992). That paper introduces the innovation of treating as multi-dimensional the payoff of a player with a quota greater than one. This is done for the many-to-many matching model with additively separable utilities, for which the stability concept is defined. It is then proved, via linear programming, that the set of stable outcomes is nonempty and it may be strictly bigger than the set of dual solutions and strictly smaller than the core. The present paper defines a general concept of stability and shows that this concept is a natural solution concept, stronger than the core concept, for a much more general coalitional game than a matching game. Instead of mutual agreements inside partnerships, the players are allowed to make collective agreements inside coalitions of any size and to distribute his labor among them. A collective agreement determines the level of labor at which the coalition operates and the division, among its members, of the income generated by the coalition. An allocation specifies a set of collective agreements for each player.

The frontal assessment battery (FAB) reveals neurocognitive dysfunction in substance-dependent individuals in distinct executive domains: Abstract reasoning, motor programming, and cognitive flexibility

Substance-dependence is highly associated with executive cognitive function (ECF) impairments. However. considering that it is difficult to assess ECF clinically, the aim of the present study was to examine the feasibility of a brief neuropsychological tool (the Frontal Assessment Battery FAB) to detect specific ECF impairments in a sample of substance-dependent individuals (SDI). Sixty-two subjects participated in this study. Thirty DSM-IV-diagnosed SDI, after 2 weeks of abstinence, and 32 healthy individuals (control group) were evaluated with FAD and other ECF-related tasks: digits forward (DF), digits backward (DB), Stroop Color Word Test (SCWT), and Wisconsin Card Sorting Test (WCST). SDI did not differ from the control group on sociodemographic variables or IQ. However, SDI performed below the controls in OF, DB, and FAB. The SDI were cognitively impaired in 3 of the 6 cognitive domains assessed by the FAB: abstract reasoning, motor programming, and cognitive flexibility. The FAB correlated with DF, SCWT, and WCST. In addition, some neuropsychological measures were correlated with the amount of alcohol, cannabis, and cocaine use. In conclusion, SDI performed more poorly than the comparison group on the FAB and the FAB`s results were associated with other ECF-related tasks. The results suggested a negative impact of alcohol, cannabis, and cocaine use on the ECF. The FAB may be useful in assisting professionals as an instrument to screen for ECF-related deficits in SDI. (C) 2010 Elsevier Ltd. All rights reserved.

Recognition by toll-like receptor 2 induces antigen-presenting cell activation and Th1 programming during infection by Neospora caninum

Neospora caninum is an apicomplexan parasite responsible for major economic losses due to abortions in cattle. Toll-like receptors (TLRs) sense specific microbial products and direct downstream signaling pathways in immune cells, linking innate, and adaptive immunity. Here, we analyze the role of TLR2 on innate and adaptive immune responses during N. caninum infection. Inflammatory peritoneal macrophages and bone marrow-derived dendritic cells exposed to N. caninum-soluble antigens presented an upregulated expression of TLR2. Increased receptor expression was correlated to TLR2/MyD88-dependent antigen-presenting cell maturation and pro-inflammatory cytokine production after stimulation by antigens. Impaired innate responses observed after infection of mice genetically deficient for TLR2((-/-)) was followed by downregulation of adaptive T helper 1 (Th1) immunity, represented by diminished parasite-specific CD4(+) and CD8(+) T-cell proliferation, IFN-gamma:interleukin (IL)-10 ratio, and IgG subclass synthesis. In parallel, TLR2(-/-) mice presented higher parasite burden than wild-type (WT) mice at acute and chronic stages of infection. These results show that initial recognition of N. caninum by TLR2 participates in the generation of effector immune responses against N. caninum and imply that the receptor may be a target for future prophylactic strategies against neosporosis. Immunology and Cell Biology (2010) 88, 825-833; doi:10.1038/icb.2010.52; published online 20 April 2010

Perinatal salt restriction: A new pathway to programming adiposity indices in adult female Wistar rats

Low birth weight has been associated with increased obesity in adulthood. It has been shown that dietary salt restriction during intrauterine life induces low birth weight and insulin resistance in adult Wistar rats. The present study had a two-fold objective: to evaluate the effects that low salt intake during pregnancy and lactation has on the amount and distribution of adipose tissue; and to determine whether the phenotypic changes in fat mass in this model are associated with alterations in the activity of the renin-angiotensin system. Maternal salt restriction was found to reduce birth weight in male and female offspring. In adulthood, the female offspring of dams fed the low-salt diet presented higher adiposity indices than those seen in the offspring of dams fed a normal-salt diet. This was attributed to the fact that adipose tissue mass (retroperitoneal but not gonadal, mesenteric or inguinal) was greater in those rats than in the offspring of dams fed a normal diet. The adult offspring of dams fed the low-salt diet, compared to those dams fed a normal-salt diet, presented the following: plasma leptin levels higher in males and lower in females; plasma renin activity higher in males but not in females; and no differences in body weight, mean arterial blood pressure or serum angiotensin-converting enzyme activity. Therefore, low salt intake during pregnancy might lead to the programming of obesity in adult female offspring. (c) 2009 Elsevier Inc. All rights reserved.

An integer linear programming approach for approximate string comparison

We introduce a problem called maximum common characters in blocks (MCCB), which arises in applications of approximate string comparison, particularly in the unification of possibly erroneous textual data coming from different sources. We show that this problem is NP-complete, but can nevertheless be solved satisfactorily using integer linear programming for instances of practical interest. Two integer linear formulations are proposed and compared in terms of their linear relaxations. We also compare the results of the approximate matching with other known measures such as the Levenshtein (edit) distance. (C) 2008 Elsevier B.V. All rights reserved.

Evolutionary model trees for handling continuous classes in machine learning

Model trees are a particular case of decision trees employed to solve regression problems. They have the advantage of presenting an interpretable output, helping the end-user to get more confidence in the prediction and providing the basis for the end-user to have new insight about the data, confirming or rejecting hypotheses previously formed. Moreover, model trees present an acceptable level of predictive performance in comparison to most techniques used for solving regression problems. Since generating the optimal model tree is an NP-Complete problem, traditional model tree induction algorithms make use of a greedy top-down divide-and-conquer strategy, which may not converge to the global optimal solution. In this paper, we propose a novel algorithm based on the use of the evolutionary algorithms paradigm as an alternate heuristic to generate model trees in order to improve the convergence to globally near-optimal solutions. We call our new approach evolutionary model tree induction (E-Motion). We test its predictive performance using public UCI data sets, and we compare the results to traditional greedy regression/model trees induction algorithms, as well as to other evolutionary approaches. Results show that our method presents a good trade-off between predictive performance and model comprehensibility, which may be crucial in many machine learning applications. (C) 2010 Elsevier Inc. All rights reserved.