Mathematical Programming, ISSN 0025-5610, 3/2016, Volume 156, Issue 1, pp. 433 - 484

In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum...

68W20 | 68W40 | 65K05 | Theoretical, Mathematical and Computational Physics | 68W10 | 90C06 | Mathematics | Big data optimization | Parallel coordinate descent | Iteration complexity | 49M20 | Mathematical Methods in Physics | Partial separability | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Expected separable over-approximation | Huge-scale optimization | LASSO | 49M27 | Combinatorics | Composite objective | MATHEMATICS, APPLIED | ALGORITHM | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | CONVERGENCE | CONSTRAINTS | Big data | Algorithms | Multiprocessing | Analysis | Methods | Studies | Optimization techniques | Computer programming | Mathematical analysis | Blocking | Serials | Mathematical models | Iterative methods | Processors | Descent | Optimization

68W20 | 68W40 | 65K05 | Theoretical, Mathematical and Computational Physics | 68W10 | 90C06 | Mathematics | Big data optimization | Parallel coordinate descent | Iteration complexity | 49M20 | Mathematical Methods in Physics | Partial separability | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Expected separable over-approximation | Huge-scale optimization | LASSO | 49M27 | Combinatorics | Composite objective | MATHEMATICS, APPLIED | ALGORITHM | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | CONVERGENCE | CONSTRAINTS | Big data | Algorithms | Multiprocessing | Analysis | Methods | Studies | Optimization techniques | Computer programming | Mathematical analysis | Blocking | Serials | Mathematical models | Iterative methods | Processors | Descent | Optimization

Journal Article

Formalized Mathematics, ISSN 1426-2630, 04/2019, Volume 27, Issue 1, pp. 87 - 91

In this article we formalize in Mizar [1], [2] the maximum number of steps taken by some number theoretical algorithms, “right–to–left binary algorithm” for...

algorithms | 68W40 | Euclidean algorithm | power residues | 11A15 | 03B35 | 11A05

algorithms | 68W40 | Euclidean algorithm | power residues | 11A15 | 03B35 | 11A05

Journal Article

Journal of Fourier Analysis and Applications, ISSN 1069-5869, 12/2008, Volume 14, Issue 5, pp. 629 - 654

Sparse signal expansions represent or approximate a signal using a small number of elements from a large collection of elementary waveforms. Finding the...

68W40 | Signal, Image and Speech Processing | Mathematics | 68W25 | 90C27 | 15A29 | Abstract Harmonic Analysis | Iterative thresholding | 41A46 | Fourier Analysis | Sparse approximations | ℓ 0 regularisation | Approximations and Expansions | Applications of Mathematics | Subset selection | Partial Differential Equations | MATHEMATICS, APPLIED | MATCHING PURSUITS | l regularisation | ALGORITHM | Equipment and supplies | Algorithms | Universities and colleges | Image processing | Mathematical optimization

68W40 | Signal, Image and Speech Processing | Mathematics | 68W25 | 90C27 | 15A29 | Abstract Harmonic Analysis | Iterative thresholding | 41A46 | Fourier Analysis | Sparse approximations | ℓ 0 regularisation | Approximations and Expansions | Applications of Mathematics | Subset selection | Partial Differential Equations | MATHEMATICS, APPLIED | MATCHING PURSUITS | l regularisation | ALGORITHM | Equipment and supplies | Algorithms | Universities and colleges | Image processing | Mathematical optimization

Journal Article

Journal of Intelligent Systems, ISSN 0334-1860, 02/2019, Volume 29, Issue 1, pp. 1226 - 1234

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 4/2015, Volume 25, Issue 2, pp. 753 - 822

We consider a class of nonlinear mappings FA,N in ℝN indexed by symmetric random matrices A ∈ ℝN×N with independent entries. Within spin glass theory, special...

Polytope neighborliness | Random matrices | Message passing | Universality | Compressed sensing | polytope neighborliness | message passing | compressed sensing | random matrices | EQUATIONS | STATISTICS & PROBABILITY | NEIGHBORLINESS | Probability | Mathematics | 68W40 | 60F05

Polytope neighborliness | Random matrices | Message passing | Universality | Compressed sensing | polytope neighborliness | message passing | compressed sensing | random matrices | EQUATIONS | STATISTICS & PROBABILITY | NEIGHBORLINESS | Probability | Mathematics | 68W40 | 60F05

Journal Article

International Journal of Computer Mathematics, ISSN 0020-7160, 12/2017, Volume 94, Issue 12, pp. 2481 - 2491

The nonconvex regularization, which has superiority on sparsity-inducing over the convex counterparts, has been proposed in many areas of engineering and...

sparse signal recovery | 68W40 | 45Q05 | 90C30 | regularization | Compressed sensing | thresholding algorithm | nonlinear optimization

sparse signal recovery | 68W40 | 45Q05 | 90C30 | regularization | Compressed sensing | thresholding algorithm | nonlinear optimization

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 09/2015, Volume 84, Issue 295, pp. 2351 - 2359

The Brent-McMillan algorithm B3 (1980), when implemented with binary splitting, is the fastest known algorithm for high-precision computation of Euler's...

MATHEMATICS, APPLIED | Mathematics - Numerical Analysis

MATHEMATICS, APPLIED | Mathematics - Numerical Analysis

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 8/2008, Volume 18, Issue 4, pp. 1351 - 1378

Let $(X_{n}\colon n\geq 0)$ be a sequence of i.i.d. r.v.'s with negative mean. Set S₀ = 0 and define $S_{n}=X_{1}+\cdots +X_{n}$. We propose an importance...

Estimate reliability | Approximation | Algorithms | Random walk | Insurance risk | Random variables | Traffic estimation | Sampling distributions | Estimators | Probabilities | Single-server queue | Change-of-measure | Random walks | Rare-event simulation | State-dependent importance sampling | Heavy-tails | Lyapunov bounds | MONTE-CARLO | random walks | rare-event simulation | change-of-measure | STATISTICS & PROBABILITY | heavy-tails | single-server queue | state-dependent importance sampling | Mathematics - Probability | 60J20 | 68W40 | 60G50 | 60G70 | 60J05

Estimate reliability | Approximation | Algorithms | Random walk | Insurance risk | Random variables | Traffic estimation | Sampling distributions | Estimators | Probabilities | Single-server queue | Change-of-measure | Random walks | Rare-event simulation | State-dependent importance sampling | Heavy-tails | Lyapunov bounds | MONTE-CARLO | random walks | rare-event simulation | change-of-measure | STATISTICS & PROBABILITY | heavy-tails | single-server queue | state-dependent importance sampling | Mathematics - Probability | 60J20 | 68W40 | 60G50 | 60G70 | 60J05

Journal Article

Groups Complexity Cryptology, ISSN 1867-1144, 11/2016, Volume 8, Issue 2, pp. 91 - 107

Given a computational model with registers of that is equipped with the set of unit cost operations, and given a safe prime number , we present the first...

68Q25 | 68W40 | 11Y16 | Fermat quotient | Cryptography | discrete logarithm problem | cyclicintegers

68Q25 | 68W40 | 11Y16 | Fermat quotient | Cryptography | discrete logarithm problem | cyclicintegers

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 12/2019, Volume 62, Issue 4, pp. 879 - 911

We give algorithms with running time $$2^{\mathcal {O}({\sqrt{k}\log {k}})} \cdot n^{\mathcal {O}(1)}$$ 2 O ( k log k ) · n O ( 1 ) for the following problems....

68Q25 | Computational Mathematics and Numerical Analysis | 68W40 | Feedback vertex set | 68W01 | Mathematics | Longest cycle | Unit square graph | Longest path | Cycle packing | Combinatorics | Unit disk graph | Parameterized complexity | Theorems | Algorithms | Apexes | Run time (computers) | Graphs | Separators | Markov analysis

68Q25 | Computational Mathematics and Numerical Analysis | 68W40 | Feedback vertex set | 68W01 | Mathematics | Longest cycle | Unit square graph | Longest path | Cycle packing | Combinatorics | Unit disk graph | Parameterized complexity | Theorems | Algorithms | Apexes | Run time (computers) | Graphs | Separators | Markov analysis

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2017, Volume 86, Issue 304, pp. 985 - 1003

Let \psi _m be the smallest strong pseudoprime to the first m prime bases. This value is known for 1 \leq m \leq 11. We extend this by finding \psi _{12} and...

MATHEMATICS, APPLIED | GCD

MATHEMATICS, APPLIED | GCD

Journal Article

Mathematics of operations research, ISSN 0364-765X, 8/2016, Volume 41, Issue 3, pp. 851 - 864

Two important characteristics encountered in many real-world scheduling problems are heterogeneous processors and a certain degree of uncertainty about the...

approximation algorithm | linear programming relaxation | stochastic scheduling | EWI-27086 | 90B36, 68M20, 90C27, 90C59, 68W25, 68W40, 68Q25 | METIS-317229 | minsum objective | Approximation Algorithm | IR-100710 | unrelated machines | Stochastic Scheduling | Linear programming relaxation | Approximation algorithm | Stochastic scheduling | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION | WEIGHTED COMPLETION-TIME | Scheduling (Management) | Usage | Stochastic processes | Analysis

approximation algorithm | linear programming relaxation | stochastic scheduling | EWI-27086 | 90B36, 68M20, 90C27, 90C59, 68W25, 68W40, 68Q25 | METIS-317229 | minsum objective | Approximation Algorithm | IR-100710 | unrelated machines | Stochastic Scheduling | Linear programming relaxation | Approximation algorithm | Stochastic scheduling | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION | WEIGHTED COMPLETION-TIME | Scheduling (Management) | Usage | Stochastic processes | Analysis

Journal Article

Journal of Applied Probability, ISSN 0021-9002, 09/2012, Volume 49, Issue 3, pp. 795 - 805

Estimator algorithms in learning automata are useful tools for adaptive, real-time optimization in computer science and engineering applications. In this paper...

Indirect estimator algorithm | Convergence | Learning automaton | Computer Science - Learning | 68W27 | 68W40 | learning automaton | indirect estimator algorithm | 68Q87

Indirect estimator algorithm | Convergence | Learning automaton | Computer Science - Learning | 68W27 | 68W40 | learning automaton | indirect estimator algorithm | 68Q87

Journal Article

Mathematical Programming, ISSN 0025-5610, 11/2018, Volume 172, Issue 1, pp. 209 - 229

Given a bipartite graph $$G = (A \cup B,E)$$ G=(A∪B,E) with strict preference lists and given an edge $$e^* \in E$$ e∗∈E , we ask if there exists a popular...

68W40 | Theoretical, Mathematical and Computational Physics | 05C85 | Mathematics | 05C70 | Matching under preferences | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Popular matching | Numerical Analysis | Dominant matching | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STABLE MARRIAGE PROBLEM | Algorithms | Matching | Graph theory

68W40 | Theoretical, Mathematical and Computational Physics | 05C85 | Mathematics | 05C70 | Matching under preferences | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Popular matching | Numerical Analysis | Dominant matching | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STABLE MARRIAGE PROBLEM | Algorithms | Matching | Graph theory

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 9/2018, Volume 71, Issue 1, pp. 221 - 250

Multiplicative update rules are a well-known computational method for nonnegative matrix factorization. Depending on the error measure between two matrices,...

Global convergence | 68W40 | Nonnegative matrix factorization | Mathematics | Statistics, general | Optimization | Multiplicative update rule | 90C30 | 15A23 | Operations Research/Decision Theory | Convex and Discrete Geometry | 90C90 | Operations Research, Management Science | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHMS | DIVERGENCE | Factorization | Error analysis | Convergence

Global convergence | 68W40 | Nonnegative matrix factorization | Mathematics | Statistics, general | Optimization | Multiplicative update rule | 90C30 | 15A23 | Operations Research/Decision Theory | Convex and Discrete Geometry | 90C90 | Operations Research, Management Science | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHMS | DIVERGENCE | Factorization | Error analysis | Convergence

Journal Article

GEM - International Journal on Geomathematics, ISSN 1869-2672, 12/2019, Volume 10, Issue 1, pp. 1 - 28

A new approach for flow simulation in very complex discrete fracture networks based on PDE-constrained optimization has been recently proposed in...

68U20 | 68W40 | 86A05 | 68W10 | Mathematics | Earth Sciences, general | Computational Science and Engineering | Simulations in complex geometries | GPGPU | CUDA | Discrete fracture network flow simulations | 86-08 | Applications of Mathematics | 65N30

68U20 | 68W40 | 86A05 | 68W10 | Mathematics | Earth Sciences, general | Computational Science and Engineering | Simulations in complex geometries | GPGPU | CUDA | Discrete fracture network flow simulations | 86-08 | Applications of Mathematics | 65N30

Journal Article

The Annals of Statistics, ISSN 0090-5364, 2/2011, Volume 39, Issue 1, pp. 333 - 361

We study the rates of convergence in generalization error achievable by active learning under various types of label noise. Additionally, we study the general...

Error rates | Minimax | Active learning | Learning rate | Machine learning | Mathematical functions | Entropy | Learning theory | Coefficients | Learning styles | Sequential design | Model selection | Selective sampling | Classification | Statistical learning theory | Oracle inequalities | selective sampling | oracle inequalities | EMPIRICAL PROCESSES | INEQUALITIES | BOUNDS | sequential design | statistical learning theory | model selection | STATISTICS & PROBABILITY | classification | SAMPLE MODULI | 68Q25 | 68T10 | 68W40 | 68T05 | 62L05 | 62H30 | 62G99 | 68Q32 | 68Q10

Error rates | Minimax | Active learning | Learning rate | Machine learning | Mathematical functions | Entropy | Learning theory | Coefficients | Learning styles | Sequential design | Model selection | Selective sampling | Classification | Statistical learning theory | Oracle inequalities | selective sampling | oracle inequalities | EMPIRICAL PROCESSES | INEQUALITIES | BOUNDS | sequential design | statistical learning theory | model selection | STATISTICS & PROBABILITY | classification | SAMPLE MODULI | 68Q25 | 68T10 | 68W40 | 68T05 | 62L05 | 62H30 | 62G99 | 68Q32 | 68Q10

Journal Article

Scientometrics, ISSN 0138-9130, 9/2013, Volume 96, Issue 3, pp. 845 - 864

In the paper we show that the bibliographic data can be transformed into a collection of compatible networks. Using network multiplication different...

68W40 | Two-mode network | Information Storage and Retrieval | Sparse network | Network multiplication | 93A15 | Interdisciplinary Studies | 91D30 | Collaboration | Computer Science | 62H30 | Library Science | Normalization | Co-authorship | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INFORMATION SCIENCE & LIBRARY SCIENCE | COCITATION | Social networks | Analysis

68W40 | Two-mode network | Information Storage and Retrieval | Sparse network | Network multiplication | 93A15 | Interdisciplinary Studies | 91D30 | Collaboration | Computer Science | 62H30 | Library Science | Normalization | Co-authorship | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INFORMATION SCIENCE & LIBRARY SCIENCE | COCITATION | Social networks | Analysis

Journal Article

Combinatorics Probability and Computing, ISSN 0963-5483, 2018, Volume 28, Issue 4, pp. 485 - 518

We present an average-case analysis of a variant of dual-pivot quicksort. We show that the algorithmic partitioning strategy used is optimal, that is, it...

2010 Mathematics subject classification | 68Q25 | 68W40 | Primary 05A16 | Secondary 68R05 | 68P10 | MATHEMATICS | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | Combinatorial analysis | Optimization

2010 Mathematics subject classification | 68Q25 | 68W40 | Primary 05A16 | Secondary 68R05 | 68P10 | MATHEMATICS | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | Combinatorial analysis | Optimization

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 10/2014, Volume 24, Issue 5, pp. 2143 - 2175

In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable...

Mathematical sequences | Mathematical theorems | Algorithms | Random walk | Markov chains | Recursion | Estimators | Point estimators | Perceptron convergence procedure | Ruin theory with stochastic investments | Last exit times | Perpetuities | Regeneration times | Risk theory | First entrance times | Large deviations | Financial time series | Nonlinear renewal theory | Harris recurrent Markov chains | Monte Carlo methods | ARCH processes | GARCH processes | Importance sampling | large deviations | ruin theory | risk theory | regeneration times | RENEWAL THEORY | STATISTICS & PROBABILITY | importance sampling | first entrance times | RUIN | financial time series | with stochastic investments | last exit times | nonlinear renewal theory | perpetuities | 60K20 | 68W40 | 68U20 | 60G40 | 91G60 | 60J05 | 60H25 | 60J22 | 60J10 | ruin theory with stochastic investments | 60F10 | 60G70 | 91G70 | 91B70 | 60K15 | 65C05 | 91B30

Mathematical sequences | Mathematical theorems | Algorithms | Random walk | Markov chains | Recursion | Estimators | Point estimators | Perceptron convergence procedure | Ruin theory with stochastic investments | Last exit times | Perpetuities | Regeneration times | Risk theory | First entrance times | Large deviations | Financial time series | Nonlinear renewal theory | Harris recurrent Markov chains | Monte Carlo methods | ARCH processes | GARCH processes | Importance sampling | large deviations | ruin theory | risk theory | regeneration times | RENEWAL THEORY | STATISTICS & PROBABILITY | importance sampling | first entrance times | RUIN | financial time series | with stochastic investments | last exit times | nonlinear renewal theory | perpetuities | 60K20 | 68W40 | 68U20 | 60G40 | 91G60 | 60J05 | 60H25 | 60J22 | 60J10 | ruin theory with stochastic investments | 60F10 | 60G70 | 91G70 | 91B70 | 60K15 | 65C05 | 91B30

Journal Article

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