Improving ultimate convergence of an augmented Lagrangian method

Optimization methods that employ the classical Powell-Hestenes-Rockafellar augmented Lagrangian are useful tools for solving nonlinear programming problems. Their reputation decreased in the last 10 years due to the comparative success of interior-point Newtonian algorithms, which are asymptotically faster. In this research, a combination of both approaches is evaluated. The idea is to produce a competitive method, being more robust and efficient than its `pure` counterparts for critical problems. Moreover, an additional hybrid algorithm is defined, in which the interior-point method is replaced by the Newtonian resolution of a Karush-Kuhn-Tucker (KKT) system identified by the augmented Lagrangian algorithm. The software used in this work is freely available through the Tango Project web page:http://www.ime.usp.br/similar to egbirgin/tango/.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES

Consider a continuous-time Markov process with transition rates matrix Q in the state space Lambda boolean OR {0}. In In the associated Fleming-Viot process N particles evolve independently in A with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Lambda is finite, we show that the empirical distribution of the particles at a fixed time converges as N -> infinity to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N -> infinity to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1/N.

Tilt-critical algebras of tame type

Let A be a finite dimensional k-algebra over an algebraically closed field. Assume A=kQ/I where Q is a quiver without oriented cycles. We say that A is tilt-critical if it is not tilted but every proper convex subcategory of A is tilted. We describe the tilt-critical algebras which are strongly simply connected and tame.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

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.

Synthesis and Characterization of Magnetic Composites Based on Cis-Polyisoprene and CoFe(2)O(4) Nanoparticles

CoFe(2)O(4) nanoparticles were obtained by the co-precipitation method. They were further modified by the adsorption of ricinoleic acid (RA). The non-modified and modified CoFe(2)O(4)/RA nanoparticles were characterized by transmission electron microscopy (TEM), atomic force microscopy (AFM), Raman, and Fourier transform infrared (FTIR) spectroscopy. The modified particles present a mean diameter < 20 nm. The adsorption of RA on the CoFe(2)O(4) surface is characterized by the IR absorptions of the RA while in the Raman spectrum the predominant signals are those from the CoFe(2)O(4). The cis-polyisoprene (PI) composite was prepared by dissolving PI in cyclohexane followed by the addition of a magnetic fluid based on CoFe(2)O(4)/RA nanoparticles dispersed in cyclohexane. After solvent evaporation a magnetic composite was obtained and characterized by AFM, Raman, and FTIR measurements. AFM images show uniformly CoFe(2)O(4)/RA particles distributed in the PI matrix. Raman spectra obtained for the composites reveal the characteristic Raman peaks of PI and CoFe(2)O(4) nanoparticles.

Thin films of xyloglucans for BSA adsorption

In this work. XG extracted from Tamarindus indica (XGT) and Copaifera langsdorffii (XGC) seeds were deposited onto Si wafers as thin films. The characteristics of XGT and XGC adsorbed layers were compared with a commercial XG sample (TKP, Tamarind kernel powder) by ellipsometry, and atomic force microscopy (AFM). Moreover, the adsorption of oxidized derivative of XGT (To60) onto amino-terminated Si wafers and the immobilization of bovine serum albumin (BSA) onto polysaccharides covered wafers, as a function of pH, were also investigated. The XG samples presented molar ratios Glc:Xyl:Gal of 2.4:2.1:1 (XGC) 2.8: 23: 1 (XGT) and 1.91.91 (TKP). The structure of XGT and XGC was determined by O-methy alditol acetate derivatization and showed similar features, but XGC confirmed the presence of more alpha-D-Xyl branches due to more beta-D-Gal ends. XGT deposited onto Si adsorbed as fibers and small entities uniformly distributed, as evidenced by AFM, while TPK and XGC formed larger aggregates. The thickness of To60 onto amino-terminated surface was similar to that determined for XGT onto Si wafers. A maximum in the adsorbed amount of BSA occurred close to its isoelectric point (5.5). These findings indicate that XGT and To60 are potential materials for the development of biomaterials and biotechnological devices. (C) 2008 Elsevier B.V. All rights reserved.

Ex Situ Scanning Electrochemical Microscopy (SECM) Investigation of Bismuth- and Bismuth/Lead Alloy Film-Modified Gold Electrodes in Alkaline Medium

Scanning electrochemical microscopy (SECM) in feedback mode was employed to characterise the reactivity and microscopic peculiarities of bismuth and bismuth/lead alloys plated onto gold disk substrates in 0.1 molL(-1) NaOH solutions. Methyl viologen was used as redox mediator, while a platinum microelectrode was employed as the SECM tip. The metal films were electrodeposited ex situ from NaOH solutions containing either bismuth ions only or both bismuth and lead ions. Approach curves and SECM images indicated that the metal films were conductive and locally reactive with oxygen to provide Bi(3+) and Pb(2+) ions. The occurrence of the latter chemical reactions was verified by local anodic stripping voltammetry (ASV) at the substrate solution interface by using a mercury-coated platinum SECM tip. The latter types of measurements allowed also verifying that lead was not uniformly distributed onto the bismuth film electrode substrate. These findings were confirmed by scanning electron microscopy images. The surface heterogeneity produced during the metal deposition process, however, did not affect the analytical performance of the bismuth coated gold electrode in anodic stripping voltammetry for the determination of lead in alkaline media, even in aerated aqueous solutions. Under the latter conditions, stripping peak currents proportional to lead concentration with a satisfactory reproducibility (within 5% RSD) were obtained.

Electrodeposition and characterization of undoped and nitrogen-doped ZnSe films

Semiconducting films of (n-type) ZnSe and (p-type) nitrogen-doped ZnSe were electrodeposited by a linear-sweep voltammetric technique on to a substrate of fluorine-tin oxide (FM) glass ceramics. The films were characterized by scanning electron microscopy, energy-dispersive X-ray analysis and grazing-incidence X-ray diffraction. The results indicated that the material was deposited uniformly over the substrate, forming clusters when the Zn content of the bath was 0.1 mol L(-1) and a film when it was 0.2 or 0.3 mol L(-1). The effectiveness of doping the films with nitrogen by adding ammonium sulfate to the deposition solution was assessed by measuring the film-electrolyte interface capacitance (C) at various applied potentials (E(ap)) and plotting Mott-Schottky curves (C(-2) vs E(ap)), whose slope sign was used to identify p-type ZnSe. (C) 2009 Elsevier B.V. All rights reserved.

Computational study of the step size parameter of the subgradient optimization method

The subgradient optimization method is a simple and flexible linear programming iterative algorithm. It is much simpler than Newton's method and can be applied to a wider variety of problems. It also converges when the objective function is non-differentiable. Since an efficient algorithm will not only produce a good solution but also take less computing time, we always prefer a simpler algorithm with high quality. In this study a series of step size parameters in the subgradient equation is studied. The performance is compared for a general piecewise function and a specific p-median problem. We examine how the quality of solution changes by setting five forms of step size parameter.

O método de Perron : aplicações e extensões

Nesta dissertação apresentamos e desenvolvemos o Método de Perron, fazendo uma aplicação ao ploblema de Dirichlet para a equação das superfícies de curvatura média constante em R3. Apresentamos também uma extensão deste método dentro de EDP's e, por fim, obtemos uma extensão geométrica que se aplica a superfícies ao invés de gráficos. Comentamos a aplicação deste método geométrico á existência de superfícies mínimas tendo como bordo duas curvas convexas em planos paralelos do R3.

Local concavifiability of preferences and determinacy of equilibrium

In this paper we consider strictly convex monotone continuous complete preorderings on R+n that are locally representable by a concave utility function. By Alexandroff 's (1939) theorem, this function is twice dífferentiable almost everywhere. We show that if the bordered hessian determinant of a concave utility representation vanishes on a null set. Then demand is countably rectifiable, that is, except for a null set of bundles, it is a countable union of c1 manifolds. This property of consumer demand is enough to guarantee that the equilibrium prices of apure exchange economy will be locally unique, for almost every endowment. We give an example of an economy satisfying these conditions but not the Katzner (1968) - Debreu (1970, 1972) smoothness conditions.

Bubbles, collateral and monetary equilibrium

Consider an economy where infinite-lived agents trade assets collateralized by durable goods. We obtain results that rule out bubbles when the additional endowments of durable goods are uniformly bounded away from zero, regardless of whether the asset’s net supply is positive or zero. However, bubbles may occur, even for state-price processes that generate finite present value of aggregate wealth. First, under complete markets, if the net supply is being endogenously reduced to zero as a result of collateral repossession. Secondly, under incomplete markets, for a persistent positive net supply, under the general conditions guaranteeing existence of equilibrium. Examples of monetary equilibria are provided.

Laws of large numbers for non-additive probabilities

We apply the concept of exchangeable random variables to the case of non-additive robability distributions exhibiting ncertainty aversion, and in the lass generated bya convex core convex non-additive probabilities, ith a convex core). We are able to rove two versions of the law of arge numbers (de Finetti's heorems). By making use of two efinitions. of independence we rove two versions of the strong law f large numbers. It turns out that e cannot assure the convergence of he sample averages to a constant. e then modal the case there is a true" probability distribution ehind the successive realizations of the uncertain random variable. In this case convergence occurs. This result is important because it renders true the intuition that it is possible "to learn" the "true" additive distribution behind an uncertain event if one repeatedly observes it (a sufficiently large number of times). We also provide a conjecture regarding the "Iearning" (or updating) process above, and prove a partia I result for the case of Dempster-Shafer updating rule and binomial trials.