Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

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.

Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.

TWO NEW WEAK CONSTRAINT QUALIFICATIONS AND APPLICATIONS

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.

Augmented β-cell Function And Mass In Glucocorticoid-treated Rodents Are Associated With Increased Islet Ir-β /akt/mtor And Decreased Ampk/acc And As160 Signaling.

Glucocorticoid (GC) therapies may adversely cause insulin resistance (IR) that lead to a compensatory hyperinsulinemia due to insulin hypersecretion. The increased β-cell function is associated with increased insulin signaling that has the protein kinase B (AKT) substrate with 160 kDa (AS160) as an important downstream AKT effector. In muscle, both insulin and AMP-activated protein kinase (AMPK) signaling phosphorylate and inactivate AS160, which favors the glucose transporter (GLUT)-4 translocation to plasma membrane. Whether AS160 phosphorylation is modulated in islets from GC-treated subjects is unknown. For this, two animal models, Swiss mice and Wistar rats, were treated with dexamethasone (DEX) (1 mg/kg body weight) for 5 consecutive days. DEX treatment induced IR, hyperinsulinemia, and dyslipidemia in both species, but glucose intolerance and hyperglycemia only in rats. DEX treatment caused increased insulin secretion in response to glucose and augmented β-cell mass in both species that were associated with increased islet content and increased phosphorylation of the AS160 protein. Protein AKT phosphorylation, but not AMPK phosphorylation, was found significantly enhanced in islets from DEX-treated animals. We conclude that the augmented β-cell function developed in response to the GC-induced IR involves inhibition of the islet AS160 protein activity.

Augmented Mixed Models For Clustered Proportion Data.

Often in biomedical research, we deal with continuous (clustered) proportion responses ranging between zero and one quantifying the disease status of the cluster units. Interestingly, the study population might also consist of relatively disease-free as well as highly diseased subjects, contributing to proportion values in the interval [0, 1]. Regression on a variety of parametric densities with support lying in (0, 1), such as beta regression, can assess important covariate effects. However, they are deemed inappropriate due to the presence of zeros and/or ones. To evade this, we introduce a class of general proportion density, and further augment the probabilities of zero and one to this general proportion density, controlling for the clustering. Our approach is Bayesian and presents a computationally convenient framework amenable to available freeware. Bayesian case-deletion influence diagnostics based on q-divergence measures are automatic from the Markov chain Monte Carlo output. The methodology is illustrated using both simulation studies and application to a real dataset from a clinical periodontology study.

Augmented muscle vasodilatory responses in obese children with Glu27 beta(2)-adrenoceptor polymorphism

This study examined forearm vasodilatation during mental challenge and exercise in 72 obese children (OC; age = 10 +/- 0.1 years) homozygous with polymorphism in the allele 27 of the beta(2)-adrenoceptors: Gln27 (n = 61) and Glu27 (n = 11). Forearm blood flow was recorded during 3 min of each using the Stroop color-word test (MS) and handgrip isometric exercise. Baseline hemodynamic and vascular measurements were similar. During the MS, peak forearm vascular conductance was significantly greater in group Glu27 (Delta = 0.35 +/- 0.4 vs. 0.12 +/- 0.1 units, respectively, p = .042). Similar results were found during exercise (Delta = 0.64 +/- 0.1 vs. 0.13 +/- 0.1 units, respectively, p = .035). Glu27 OC increased muscle vasodilatory responsiveness upon the MS and exercise.

Early Australian experience with infliximab, a chimeric antibody against tumour necrosis factor-alpha, in the treatment of Crohn's disease: is its efficacy augmented by steroid-sparing immunosuppressive therapy?

Background: Tumour necrosis factor-alpha (TNF-alpha) plays an important role in the pathology of Crohn's disease. Infliximab, a chimeric antibody against TNF-alpha, has been shown in controlled clinical trials to be effective in two-thirds of patients with refractory or fistulating Crohn's disease. The factors that determine a clinical response in some patients but not others are unknown. Aims: To document the early Australian experience with infliximab treatment for Crohn's disease and to identify factors that may determine a beneficial clinical response. Methods: Gastroenterologists known to have used infliximab for Crohn's disease according to a compassionate use protocol were asked to complete a spreadsheet that included demographic information, Crohn's disease site, severity, other medical or surgical treatments and a global clinical assessment of Crohn's disease outcome, judged by participating physicians as complete and sustained (remission for the duration of the study), complete but unsustained (remission at 4 weeks but not for the whole study) or partial clinical improvement (sustained or unsustained). Results: Fifty-seven patients were able to be evaluated, with a median follow-up time of 16.4 (4-70) weeks, including 23 patients with fistulae. There were 21 adverse events, including four serious events. Fifty-one patients (89%) had a positive clinical response for a median duration (range) of 11 (2-70) weeks. Thirty patients (52%) had a remission at 4 weeks, 10 of whom had remission for longer than 12 weeks. Forty-two per cent of fistulae closed. Sustained remission (P = 0.065), remission at 4 weeks (P = 0.033) and a positive clinical response of any sort (P = 0.004) were more likely in patients on immunosuppressive therapy, despite there being more smelters in this group. Conclusion: This review of the first Australian experience with infliximab corroborates the reported speed and efficacy of this treatment for Crohn's disease. The excellent response appears enhanced by the concomitant use of conventional steroid-sparing immunosuppressive therapy.

A zero-augmented gamma mixed model for longitudinal data with many zeros

In many occupational safety interventions, the objective is to reduce the injury incidence as well as the mean claims cost once injury has occurred. The claims cost data within a period typically contain a large proportion of zero observations (no claim). The distribution thus comprises a point mass at 0 mixed with a non-degenerate parametric component. Essentially, the likelihood function can be factorized into two orthogonal components. These two components relate respectively to the effect of covariates on the incidence of claims and the magnitude of claims, given that claims are made. Furthermore, the longitudinal nature of the intervention inherently imposes some correlation among the observations. This paper introduces a zero-augmented gamma random effects model for analysing longitudinal data with many zeros. Adopting the generalized linear mixed model (GLMM) approach reduces the original problem to the fitting of two independent GLMMs. The method is applied to evaluate the effectiveness of a workplace risk assessment teams program, trialled within the cleaning services of a Western Australian public hospital.

An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

Augmented Reality for Games

In this text, we intend to explore augmented reality as a means to visualise interactive communication projects. With ARToolkit, Virtools and 3ds Max applications, we aim to show how to create a portable interactive platform that resorts to the environment and markers for constructing the game’s scenario. We plan to show that the realism of simulation, together with the merger of artificial objects with the real world, can generate interactive empathy between players and their avatars.

Augmented LDPC Graph for Distributed Video Coding with Multiple Side Information

The advances made in channel-capacity codes, such as turbo codes and low-density parity-check (LDPC) codes, have played a major role in the emerging distributed source coding paradigm. LDPC codes can be easily adapted to new source coding strategies due to their natural representation as bipartite graphs and the use of quasi-optimal decoding algorithms, such as belief propagation. This paper tackles a relevant scenario in distributedvideo coding: lossy source coding when multiple side information (SI) hypotheses are available at the decoder, each one correlated with the source according to different correlation noise channels. Thus, it is proposed to exploit multiple SI hypotheses through an efficient joint decoding technique withmultiple LDPC syndrome decoders that exchange information to obtain coding efficiency improvements. At the decoder side, the multiple SI hypotheses are created with motion compensated frame interpolation and fused together in a novel iterative LDPC based Slepian-Wolf decoding algorithm. With the creation of multiple SI hypotheses and the proposed decoding algorithm, bitrate savings up to 8.0% are obtained for similar decoded quality.

GPU implementation of the simplex identification via split augmented Lagrangian

Hyperspectral imaging can be used for object detection and for discriminating between different objects based on their spectral characteristics. One of the main problems of hyperspectral data analysis is the presence of mixed pixels, due to the low spatial resolution of such images. This means that several spectrally pure signatures (endmembers) are combined into the same mixed pixel. Linear spectral unmixing follows an unsupervised approach which aims at inferring pure spectral signatures and their material fractions at each pixel of the scene. The huge data volumes acquired by such sensors put stringent requirements on processing and unmixing methods. This paper proposes an efficient implementation of a unsupervised linear unmixing method on GPUs using CUDA. The method finds the smallest simplex by solving a sequence of nonsmooth convex subproblems using variable splitting to obtain a constraint formulation, and then applying an augmented Lagrangian technique. The parallel implementation of SISAL presented in this work exploits the GPU architecture at low level, using shared memory and coalesced accesses to memory. The results herein presented indicate that the GPU implementation can significantly accelerate the method's execution over big datasets while maintaining the methods accuracy.

Parallel GPU architecture for hyperspectral unmixing based on augmented Lagrangian method

Hyperspectral imaging has become one of the main topics in remote sensing applications, which comprise hundreds of spectral bands at different (almost contiguous) wavelength channels over the same area generating large data volumes comprising several GBs per flight. This high spectral resolution can be used for object detection and for discriminate between different objects based on their spectral characteristics. One of the main problems involved in hyperspectral analysis is the presence of mixed pixels, which arise when the spacial resolution of the sensor is not able to separate spectrally distinct materials. Spectral unmixing is one of the most important task for hyperspectral data exploitation. However, the unmixing algorithms can be computationally very expensive, and even high power consuming, which compromises the use in applications under on-board constraints. In recent years, graphics processing units (GPUs) have evolved into highly parallel and programmable systems. Specifically, several hyperspectral imaging algorithms have shown to be able to benefit from this hardware taking advantage of the extremely high floating-point processing performance, compact size, huge memory bandwidth, and relatively low cost of these units, which make them appealing for onboard data processing. In this paper, we propose a parallel implementation of an augmented Lagragian based method for unsupervised hyperspectral linear unmixing on GPUs using CUDA. The method called simplex identification via split augmented Lagrangian (SISAL) aims to identify the endmembers of a scene, i.e., is able to unmix hyperspectral data sets in which the pure pixel assumption is violated. The efficient implementation of SISAL method presented in this work exploits the GPU architecture at low level, using shared memory and coalesced accesses to memory.