Multidimensional optimization algorithms numerical results

This paper presents some multidimensional optimization algorithms. By using the "penalty function" method, these algorithms are used to solving an entire class of economic optimization problems. Comparative numerical results of certain new multidimensional optimization algorithms for solving some test problems known on literature are shown.optimization algorithm, multidimensional optimization, penalty function

ABOUT RISK PROCESS ESTIMATION TECHNIQUES EMPLOYED BY A VIRTUAL ORGANIZATION WHICH IS DIRECTED TOWARDS THE INSURANCE BUSINESS

In a virtual organization directed on the insurance business, the estimations of the risk process and of the ruin probability are important concerns: for researchers, at the theoretical level, and for the management of the company, as these influence the insurer strategy. We consider the evolution over an extended period of time of the insurer surplus process. In this paper, we present some methods for the estimation of the ruin probability and for the evaluation of a reserve fund. We discuss the ruin probability with respect to: the parameters of the individual claim distribution, the load factor of premiums and the intensity parameter of the number of claims process. We analyze the model in which the premiums are computed according to the mean value principle. Also, we attempt the case when the initial capital is proportional to the expected value of the individual claim. We give numerical illustration.virtual organization, ruin probability, risk process, adjustment coefficient

Analysis of A Splitting Approach for the Parallel Solution of Linear Systems on GPU Cards

We discuss an approach for solving sparse or dense banded linear systems ${\bf A} {\bf x} = {\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\bf A} \in {\mathbb{R}}^{N \times N}$ is possibly nonsymmetric and moderately large; i.e., $10000 \leq N \leq 500000$. The ${\it split\ and\ parallelize}$(${\tt SaP}$) approach seeks to partition the matrix${\bf A}$into diagonal sub-blocks${\bf A}_i$,$i=1,\ldots,P$, which are independently factored in parallel. The solution may choose to consider or to ignore the matrices that couple the diagonal sub-blocks${\bf A}_i$. This approach, along with the Krylov subspace-based iterative method that it preconditions, are implemented in a solver called${\tt SaP::GPU}$, which is compared in terms of efficiency with three commonly used sparse direct solvers:${\tt PARDISO}$,${\tt SuperLU}$, and${\tt MUMPS}$.${\tt SaP::GPU}$, which runs entirely on the GPU except several stages involved in preliminary row-column permutations, is robust and compares well in terms of efficiency with the aforementioned direct solvers. In a comparison against Intel's${\tt MKL}$,${\tt SaP::GPU}$also fares well when used to solve dense banded systems that are close to being diagonally dominant.${\tt SaP::GPU}$ is publicly available and distributed as open source under a permissive BSD3 license.Comment: 38 page

A Complete Cyclic Proof System for Inductive Entailments in First Order Logic

International audienceIn this paper we develop a cyclic proof system for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions are quantifier-free formulae of first order logic. The proof system consists of a small set of inference rules, inspired by a top-down language inclusion algorithm for tree automata [9]. We show the proof system to be sound, in general, and complete, under certain semantic restrictions involving the set of constraints in the inductive system. Moreover, we investigate the computational complexity of checking these restrictions, when the function symbols in the logic are given the canonical Herbrand interpretation

An Entailment Checker for Separation Logic with Inductive Definitions

In this paper, we present Inductor, a checker for entailments between mutually recursive predicates, whose inductive definitions contain ground constraints belonging to the quantifier-free fragment of Separation Logic. Our tool implements a proof-search method for a cyclic proof system that we have shown to be sound and complete, under certain semantic restrictions involving the set of constraints in a given inductive system. Dedicated decision procedures from the DPLL(T)-based SMT solver CVC4 are used to establish the satisfiability of Separation Logic formulae. Given inductive predicate definitions, an entailment query, and a proof-search strategy, Inductor uses a compact tree structure to explore all derivations enabled by the strategy. A successful result is accompanied by a proof, while an unsuccessful one is supported by a counterexample

An Entailment Checker for Separation Logic with Inductive Definitions An Entailment Checker for Separation Logic with Inductive Definitions

International audienceIn this paper, we present Inductor, a checker for entailments between mutually recursive predicates, whose inductive definitions contain ground constraints belonging to the quantifier-free fragment of Separation Logic. Our tool implements a proof-search method for a cyclic proof system that we have shown to be sound and complete, under certain semantic restrictions involving the set of constraints in a given inductive system. Dedicated decision procedures from the DPLL(T)-based SMT solver CVC4 are used to establish the satisfiability of Separation Logic formu-lae. Given inductive predicate definitions, an entailment query, and a proof-search strategy, Inductor uses a compact tree structure to explore all derivations enabled by the strategy. A successful result is accompanied by a proof, while an unsuccessful one is supported by a counterexample

On the Importance of Displacement History in Soft-Body Contact Models

Two approaches are commonly used for handling frictional contact within the framework of the discrete element method (DEM). One relies on the complementarity method (CM) to enforce a nonpenetration condition and the Coulomb dry-friction model at the interface between two bodies in mutual contact. The second approach, called the penalty method (PM), invokes an elasticity argument to produce a frictional contact force that factors in the local deformation and relative motion of the bodies in contact. We give a brief presentation of a DEM-PM contact model that includes multi-time-step tangential contact displacement history. We show that its implementation in an open-source simulation capability called Chrono is capable of accurately reproducing results from physical tests typical of the field of geomechanics, i.e., direct shear tests on a monodisperse material. Keeping track of the tangential contact displacement history emerges as a key element of the model. We show that identical simulations using contact models that include either no tangential contact displacement history or only single-time-step tangential contact displacement history are unable to accurately model the direct shear test

Enforcing policies with privacy guardians

AbstractReasoning about privacy in electronic environments populated with privacy-concerned agents that exchange personal data requires control of ownership and proving the right of possession of a piece of data. The privacy policy expressed by an individual for his personal data can be enforced by a context-aware mobile agent, called alter-ego, accompanying the personal data disclosed.We discuss the first steps towards a formal framework for expressing policies on information disclosure and their integration in the behavior specification of the alter-egos, that enables characterization of an environment manipulating personal data from the privacy perspective