An Unified Computational Framework for Parameter Identification of Material Models in Finite Inelasticity

Parameter identification processes concern the determination of parameters in a material model in order to fit experimental data. We provide a distinct, unified algorithmic setting of a generic class of material models and discuss the associated gradient–based optimization problem. Gradient–based optimization algorithms need derivatives of the objective function with respect to the material parameter vector κ . In order to obtain the necessary derivatives, an analytical sensitivity analysis is pointed out for the unified class of algorithmic material models. The quality of the parameter identification is demonstrated for a representative example.     

A space decomposition scheme for maximum eigenvalue functions and its applications

In this paper, we study nonlinear optimization problems involving eigenvalues of symmetric matrices. One of the difficulties in solving these problems is that the eigenvalue functions are not differentiable when the multiplicity of the function is not one. We apply the \({\mathcal {U}}\)-Lagrangian theory to analyze the largest eigenvalue function of a convex matrix-valued mapping which extends the corresponding results for linear mapping in the literature. We also provides the formula of first-and second-order derivatives of the \({\mathcal {U}}\)-Lagrangian under mild assumptions. These theoretical results provide us new second-order information about the largest eigenvalue function along a suitable smooth manifold, and leads to a new algorithmic framework for analyzing the underlying optimization problem.     

Mathematical and Information Problems of the Elemental Analysis of a Substance and of Radiation Based on Radiological Methods of Measurement and Control

We consider mathematical and information problems of elemental analysis of a substance and of radiation based on radiological methods of measurement and control. We propose a technology for solving problems of the elemental analysis at an algorithmic level. Certain results of operation of automatic data processing systems are presented.     

Generalized pattern searches with derivative information

A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses that question with respect to Generalized Pattern Search (GPS) methods for unconstrained and linearly constrained optimization. Specifically, this paper concentrates on the GPS pollstep. Polling is done to certify the need to refine the current mesh, and it requires O(n) function evaluations in the worst case. We show that the use of derivative information significantly reduces the maximum number of function evaluations necessary for pollsteps, even to a worst case of a single function evaluation with certain algorithmic choices given here. Furthermore, we show that rather rough approximations to the gradient are sufficient to reduce the pollstep to a single function evaluation. We prove that using these less expensive pollsteps does not weaken the known convergence properties of the method, all of which depend only on the pollstep.     

An empirical study of the complexity and randomness of prediction error sequences

We investigate a population of binary mistake sequences that result from learning with parametric models of different order. We obtain estimates of their error, algorithmic complexity and divergence from a purely random Bernoulli sequence. We study the relationship of these variables to the learner’s information density parameter which is defined as the ratio between the lengths of the compressed to uncompressed files that contain the learner’s decision rule. The results indicate that good learners have a low information density ρ while bad learners have a high ρ. Bad learners generate mistake sequences that are atypically complex or diverge stochastically from a purely random Bernoulli sequence. Good learners generate typically complex sequences with low divergence from Bernoulli sequences and they include mistake sequences generated by the Bayes optimal predictor. Based on the static algorithmic interference model of [18] the learner here acts as a static structure which “scatters” the bits of an input sequence (to be predicted) in proportion to its information density ρ thereby deforming its randomness characteristics.     

Parallel asynchronous tabu search for multicommodity location-allocation with balancing requirements

We study and compare asynchronous parallelization strategies for tabu search, and evaluate the impact on performance and solution quality of some important algorithmic design parameters: number of processors, handling of exchanged information, etc. Parallelization approaches are implemented and compared by using a tabu search algorithm for multicommodity location-allocation problems with balancing requirements.     

An Algorithmic Approach for Sensitivity Analysis of Perturbed Quasi-Birth-and-Death Processes

In this paper, we present an algorithmic approach for sensitivity analysis of stationary and transient performance measures of a perturbed continuous-time level-dependent quasi-birth-and-death (QBD) process with infinitely-many levels. By developing a new LU-type RG-factorization using the censoring technique, we obtain the maximal negative inverse of the infinitesimal generator of the QBD process. The derivatives of the stationary performance measures of the QBD process can then be expressed and computed in terms of the maximal negative inverse, overcoming the computational difficulty arising from the use of group inverses of infinite size in the current literature (see Cao and Chen [11]). We also use a stochastic integral functional to study the transient performance measure of the QBD process and show how to use the algorithmic approach for its sensitivity analysis. As an example, a perturbed MAP/PH/1 queue is also analyzed.     

Constructing the gain matrix of a linear observer with given characteristics

We consider control systems with incomplete information about the phase state vector that are representable by linear difference equations. We solve the problem of algorithmic synthesis of a linear observer ensuring the required spectral properties for the state estimation error system.Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 67, pp. 140–146, 1989.     

A new version of algorithmic information theory

We present a much more concrete version of algorithmic information theory in which one can actually run on a computer the algorithms in the proofs of a number of key information-theoretic incompleteness theorems.     

Chopped and sliced cones and representations of Kac-Moody algebras

We introduce the notion of a chopped and sliced cone in combinatorial geometry and prove a structure theorem expressing the number of integral points in a slice of such a cone by means of a vector partition function. We observe that this notion applies to weight multiplicities of Kac-Moody algebras and to Clebsch-Gordan coefficients for semisimple Lie algebras. This has algorithmic applications, as we demonstrate computing some explicit examples.     

Sensitivity and stability analysis for nonlinear programming

We give a brief overview of important results in several areas of sensitivity and stability analysis for nonlinear programming, focusing initially on qualitative characterizations (e.g., continuity, differentiability and convexity) of the optimal value function. Subsequent results concern quantitative measures, in particular optimal value and solution point parameter derivative calculations, algorithmic approximations, and bounds. Our treatment is far from exhaustive and concentrates on results that hold for smooth well-structured problems.Research supported by National Science Foundation Grant ECS-86-19859 and Grant N00014-89-J-1537 Office of Naval Research.     

Disparate data fusion for protein phosphorylation prediction

New challenges in knowledge extraction include interpreting and classifying data sets while simultaneously considering related information to confirm results or identify false positives. We discuss a data fusion algorithmic framework targeted at this problem. It includes separate base classifiers for each data type and a fusion method for combining the individual classifiers. The fusion method is an extension of current ensemble classification techniques and has the advantage of allowing data to remain in heterogeneous databases. In this paper, we focus on the applicability of such a framework to the protein phosphorylation prediction problem.     

An Inexact Newton Method Derived from Efficiency Analysis

We consider solving an unconstrained optimization problem by Newton-PCG like methods in which the preconditioned conjugate gradient method is applied to solve the Newton equations. The main question to be investigated is how efficient Newton-PCG like methods can be from theoretical point of view. An algorithmic model with several parameters is established. Furthermore, a lower bound of the efficiency measure of the algorithmic model is derived as a function of the parameters. By maximizing this lower bound function, the parameters are specified and therefore an implementable algorithm is obtained. The efficiency of the implementable algorithm is compared with Newtons method by theoretical analysis and numerical experiments. The results show that this algorithm is competitive.Mathematics Subject Classification: 90C30, 65K05.This work was supported by the National Science Foundation of China Grant No. 10371131, and Hong Kong Competitive Earmarked Research Grant CityU 1066/00P from Hong Kong University Grant Council     

An Exploratory Line Search for Piecewise Differentiable Objective Functions based on Algorithmic Differentiation

Nonsmoothness is a typical characteristic of numerous objective functions in optimisation that arises from applications. The standard approach in algorithmic differentiation (AD) is to consider only differentiable functions that are defined by an evaluation program. We extend this functionality by allowing also the functions abs(), min() and max() during the function evaluation yielding piecewise differential nonlinear functions. We will define an evaluation procedure for these functions and employ ADOL-C in an adapted gradient based optimisation method that was adjusted to the special properties of the objective functions considered here. First numerical results will be presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bound constrained interval global optimization in the COCONUT Environment

We introduce a new interval global optimization method for solving bound constrained problems. The method originates from a small standalone software and is implemented in the COCONUT Environment, a framework designed for the development of complex algorithms, containing numerous state-of-the-art methods in a common software platform. The original algorithm is enhanced by various new methods implemented in COCONUT, regarding both interval function evaluations (such as first and second order derivatives with backward automatic differentiation, slopes, slopes of derivatives, bicentered forms, evaluations on the Karush–John conditions, etc.) and algorithmic elements (inclusion/exclusion boxes, local search, constraint propagation). This resulted in a substantial performance increase as compared to the original code. During the selection of the best combination of options, we performed comparison tests that gave empirical answers to long-lasting algorithmic questions (such as whether to use interval gradients or use slopes instead), that have never been studied numerically in such detail before. The new algorithm, called coco_gop_ex, was tested against the prestigious BARON software on an extensive set of bound constrained problems. We found that in addition to accepting a wider class of bound constrained problems and providing more output information (by locating all global minimizers), coco_gop_ex is competitive with BARON in terms of the solution success rates (with the exception of a set of nonlinear least squares problems), and it often outperforms BARON in running time. In particular, coco_gop_ex was around 21 % faster on average over the set of problems solved by both software systems.     

A combinatorial-probabilistic analysis of bitcoin attacks*

In 2008, Satoshi Nakamoto famously invented bitcoin, and in his (or her, or their, or its) white paper sketched an approximate formula for the probability of a successful double spending attack by a dishonest party. This was corrected by Meni Rosenfeld, who, under more realistic assumptions, gave the exact probability (missing a foundational proof); and another formula (along with foundational proof), in terms of the Incomplete Beta function, was given later by Cyril Grunspan and Ricardo Pérez-Marco, that enabled them to derive an asymptotic formula for that quantity. Using Wilf-Zeilberger algorithmic proof theory, we continue in this vein and present a recurrence equation for the above-mentioned probability of success, that enables a very fast compilation of these probabilities. We next use this recurrence to derive (in algorithmic fashion) higher-order asymptotic formulas, extending the formula of Grunspan and Pérez-Marco who did the leading term. We then study the statistical properties (expectation, variance, etc.) of the duration of a successful attack.     

Granular fuzzy models: a study in knowledge management in fuzzy modeling

In system modeling, knowledge management comes vividly into the picture when dealing with a collection of individual models. These models being considered as sources of knowledge, are engaged in some collective pursuits of a collaborative development to establish modeling outcomes of global character. The result comes in the form of a so-called granular fuzzy model, which directly reflects upon and quantifies the diversity of the available sources of knowledge (local models) involved in knowledge management. In this study, several detailed algorithmic schemes are presented along with related computational aspects associated with Granular Computing. It is also shown how the construction of information granules completed through the use of the principle of justifiable granularity becomes advantageous in the realization of granular fuzzy models and a quantification of the quality (specificity) of the results of modeling. We focus on the design of granular fuzzy models considering that the locally available models are those fuzzy rule-based. It is shown that the model quantified in terms of two conflicting criteria, that is (a) a coverage criterion expressing to which extent the resulting information granules “cover” include data and (b) specificity criterion articulating how detailed (specific) the obtained information granules are. The overall quality of the granular model is also assessed by determining an area under curve (AUC) where the curve is formed in the coverage-specificity coordinates. Numeric results are discussed with intent of displaying the most essential features of the proposed methodology and algorithmic developments.     

On the Existence of Solutions to Stochastic Mathematical Programs with Equilibrium Constraints

We generalize stochastic mathematical programs with equilibrium constraints (SMPEC) introduced by Patriksson and Wynter (Ref. 1) to allow for the inclusion of joint upper-level constraints and to change the continuity assumptions with respect to the uncertainty parameters assumed before by measurability assumptions. For this problem, we prove the existence of solutions. We discuss also algorithmic aspects of the problem, in particular the construction of an inexact penalty function for the SMPEC problem. We apply the theory to the problem of structural topology optimization.     

Computing and minimizing the relative regret in combinatorial optimization with interval data

We consider combinatorial optimization problems with uncertain parameters of the objective function, where for each uncertain parameter an interval estimate is known. It is required to find a solution that minimizes the worst-case relative regret. For minmax relative regret versions of some subset-type problems, where feasible solutions are subsets of a finite ground set and the objective function represents the total weight of elements of a feasible solution, and for the minmax relative regret version of the problem of scheduling n jobs on a single machine to minimize the total completion time, we present a number of structural, algorithmic, and complexity results. Many of the results are based on generalizing and extending ideas and approaches from absolute regret minimization to the relative regret case.