The Lanczos Method with Semi-Definite Inner Product

The spectral transformation Lanczos method is very popular for solving large scale real symmetric generalized eigenvalue problems. The method uses a special inner product so that the symmetric Lanczos method can be used. Sometimes, a semi-definite inner product must be used. This may lead to instabilities and break-down. In this paper, we suggest cures for breakdown by use of implicit restarting and the pseudo-Lanczos method.This revised version was published online in October 2005 with corrections to the Cover Date.     

Cut sharing for multistage stochastic linear programs with interstage dependency

Multistage stochastic programs with interstage independent random parameters have recourse functions that do not depend on the state of the system. Decomposition-based algorithms can exploit this structure by sharing cuts (outer-linearizations of the recourse function) among different scenario subproblems at the same stage. The ability to share cuts is necessary in practical implementations of algorithms that incorporate Monte Carlo sampling within the decomposition scheme. In this paper, we provide methodology for sharing cuts in decomposition algorithms for stochastic programs that satisfy certain interstage dependency models. These techniques enable sampling-based algorithms to handle a richer class of multistage problems, and may also be used to accelerate the convergence of exact decomposition algorithms. Research leading to this work was partially supported by the Department of Energy Contract DE-FG03-92ER25116-A002; the Office of Naval Research Contract N00014-89-J-1659; the National Science Foundation Grants ECS-8906260, DMS-8913089; and the Electric Power Research Institute Contract RP 8010-09, CSA-4O05335. This author's work was supported in part by the National Research Council under a Research Associateship at the Naval Postgraduate School, Monterey, California.     

Leakage currents in ferroelectric thin films

The main mechanisms of leakage currents in thin lead zirconate titanate (PZT) ferroelectric films prepared by the sol–gel method are discussed. Four specific regions are determined in I–V dependencies. At very weak fields (10–20 kV/cm), the current falls with the voltage increase as a result of depolarization. In the low fields region (about 70–100 kV/cm), the leakage current decreases with the decrease of voltage ramp speed and its components are the ohmic and displacement currents. In the high fields region (≥130 kV/cm), the leakage current increases with the decrease of step voltage ramp in contrast to the previous case. Possible conductivity mechanisms are the Poole– Frenkel emission and hopping conduction. In the transition region between above-mentioned ones (from 80–90 to ～130 kV/cm), an abrupt unstable increase of current is observed caused by breakdown of reverse bias Schottky barrier. Depolarization currents are studied for sol–gel PZT films prepared at different preparation conditions.     

Achieving Optical Tri-Stability Through Periodic Metal-Dielectric Structure

Abstract

Through the modified transfer matrix method, the transmission properties of a one-dimensional coupled-resonator optical waveguide structure composed of metal layers and non-linear material layers is studied. Given proper incident frequency and structure parameters, an optical tri-stability has been achieved. The effect of loss has been considered.     

Backward–forward algorithms for structured monotone inclusions in Hilbert spaces

In this paper, we study the backward–forward algorithm as a splitting method to solve structured monotone inclusions, and convex minimization problems in Hilbert spaces. It has a natural link with the forward–backward algorithm and has the same computational complexity, since it involves the same basic blocks, but organized differently. Surprisingly enough, this kind of iteration arises when studying the time discretization of the regularized Newton method for maximally monotone operators. First, we show that these two methods enjoy remarkable involutive relations, which go far beyond the evident inversion of the order in which the forward and backward steps are applied. Next, we establish several convergence properties for both methods, some of which were unknown even for the forward–backward algorithm. This brings further insight into this well-known scheme. Finally, we specialize our results to structured convex minimization problems, the gradient-projection algorithms, and give a numerical illustration of theoretical interest.     

Parametric methods in integer linear programming

In contrast to methods of parametric linear programming which were developed soon after the invention of the simplex algorithm and are easily included as an extension of that method, techniques for parametric analysis on integer programs are not well known and require considerable effort to append them to an integer programming solution algorithm.The paper reviews some of the theory employed in parametric integer programming, then discusses algorithmic work in this area over the last 15 years when integer programs are solved by different methods. A summary of applications is included and the article concludes that parametric integer programming is a valuable tool of analysis awaiting further popularization.     

A New Gradient Method with an Optimal Stepsize Property

The gradient method for the symmetric positive definite linear system is as follows

Symmetrized-lexicographic order and the method of points

A variant of lexicographic order called symmetrized-lexicographic order is defined. The symmetrized-lexicographic order finds its application in the goal programming procedure called the method of points. The symmetrized-lexicographic order is shown to be representable using linear algebra and, thus, the method of points can be implemented as a linear programming problem.     

Growth mechanism and optical property of CdS nanoparticles synthesized using amino-acid histidine as chelating agent under sonochemical process

Using amino-acid histidine as chelating agent, CdS nanoparticles have been synthesized by sonochemical method. It is found that by varying the ultrasonic irradiation time, we can tune the band gap and particle size of CdS nanoparticles. The imidazole ring of histidine captures the Cd ions from the solution, and prevents the growth of the CdS nanoparticles. The deviation in the linear relation in between cube of radius of nanoparticles and ultrasonic irradiation time confirms the growth of CdS nanoparticles occur via two process; one is the diffusion process of the reactants as well as reaction at the surface of the crystallite. CdS nanoparticles synthesized using histidine as organic chelating agent have band edge emission at 481 nm and have greater photoluminescence intensity with blue-shift to higher energy due to typical quantum confinement effect.     

A strong bound on the integral of the central path curvature and its relationship with the iteration-complexity of primal-dual path-following LP algorithms

The main goals of this paper are to: i) relate two iteration-complexity bounds derived for the Mizuno-Todd-Ye predictor-corrector (MTY P-C) algorithm for linear programming (LP), and; ii) study the geometrical structure of the LP central path. The first iteration-complexity bound for the MTY P-C algorithm considered in this paper is expressed in terms of the integral of a certain curvature function over the traversed portion of the central path. The second iteration-complexity bound, derived recently by the authors using the notion of crossover events introduced by Vavasis and Ye, is expressed in terms of a scale-invariant condition number associated with m × n constraint matrix of the LP. In this paper, we establish a relationship between these bounds by showing that the first one can be majorized by the second one. We also establish a geometric result about the central path which gives a rigorous justification based on the curvature of the central path of a claim made by Vavasis and Ye, in view of the behavior of their layered least squares path following LP method, that the central path consists of long but straight continuous parts while the remaining curved part is relatively “short”. R. D. C. Monteiro was supported in part by NSF Grants CCR-0203113 and CCF-0430644 and ONR grant N00014-05-1-0183. T. Tsuchiya was supported in part by Japan-US Joint Research Projects of Japan Society for the Promotion of Science “Algorithms for linear programs over symmetric cones” and the Grants-in-Aid for Scientific Research (C) 15510144 of Japan Society for the Promotion of Science.