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Results 1 - 10
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28,644
Instance-Based First-Order Methods Using . . .
, 1997
"... Early refutational theorem proving procedures were direct applications of Herbrand's version of the completeness theorem for first-order logic. These instance-based theorem provers created propositional instances of the first-order clauses to be proved unsatisfiable, and tested the instances o ..."
Abstract
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, unification has been incorporated in creating instances of first-order clauses. Furthermore, high-performance propositional calculus provers have been developed in the past few years. As a result, it is possible to realize effective instance-based first-order methods for several applications. We describe
First-order methods for sparse covariance selection
- SIAM Journal on Matrix Analysis and Applications
"... Abstract. Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight conditional independence relationships between the ..."
Abstract
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Cited by 104 (2 self)
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the sample variables. We first formulate a convex relaxation of this combinatorial problem, we then detail two efficient first-order algorithms with low memory requirements to solve large-scale, dense problem instances.
An Accelerated First-Order Method for Solving Unconstrained Polynomial Optimization Problems
, 2011
"... Our interest lies in solving large-scale unconstrained polynomial optimization problems. Because interior-point methods for solving these problems are severely limited by the large-scale, we are motivated to explore efficient implementations of an accelerated first-order method to solve this class o ..."
Abstract
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Cited by 1 (0 self)
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Our interest lies in solving large-scale unconstrained polynomial optimization problems. Because interior-point methods for solving these problems are severely limited by the large-scale, we are motivated to explore efficient implementations of an accelerated first-order method to solve this class
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
, 2009
"... Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by recent breakthroughs in the development of novel first-order ..."
Abstract
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Cited by 171 (2 self)
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Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by recent breakthroughs in the development of novel first-order
Randomized First-Order Methods for Saddle Point Optimization *
"... Abstract In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an O(1/N ) and O(1/N 2 ) rate of convergence, respectively, for general bilinear saddle point an ..."
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are equivalent to certain randomized variants of the alternating direction method of multipliers (ADMM), while a direct extension of ADMM does not necessarily converge when the number of blocks exceeds two.
Stochastic first order methods in smooth convex optimization
, 2011
"... In this paper, we are interested in the development of efficient first-order methods for convex optimization problems in the simultaneous presence of smoothness of the objective function and stochasticity in the first-order information. First, we consider the Stochastic Primal Gradient method, which ..."
Abstract
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Cited by 7 (0 self)
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In this paper, we are interested in the development of efficient first-order methods for convex optimization problems in the simultaneous presence of smoothness of the objective function and stochasticity in the first-order information. First, we consider the Stochastic Primal Gradient method
First Order Methods for Large-Scale Sparse Optimization
, 2011
"... In today’s digital world, improvements in acquisition and storage technology are allowing us to acquire more accurate and finer application-specific data, whether it be tick-by-tick price data from the stock market or frame-by-frame high resolution images and videos from surveillance systems, remote ..."
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dense and ill-conditioned data matrices. Therefore, interior point based methods are ill-suited for solving these problems. The large scale of these problems forces one to use the so-called first-order methods that only use gradient information at each iterate. These methods are efficient for problems
Faster First-Order Methods for Extensive-Form Game Solving
, 2015
"... We study the problem of computing a Nash equilibrium in large-scale two-player zero-sum extensive-form games. While this problem can be solved in polynomial time, first-order or regret-based methods are usually preferred for large games. Regret-based methods have largely been favored in practice, in ..."
Abstract
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Cited by 1 (1 self)
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We study the problem of computing a Nash equilibrium in large-scale two-player zero-sum extensive-form games. While this problem can be solved in polynomial time, first-order or regret-based methods are usually preferred for large games. Regret-based methods have largely been favored in practice
Primal-dual First-order Methods with O(1/) Iterationcomplexity for Cone Programming
"... In this paper we consider the general cone programming problem, and propose primal-dual convex (smooth and/or nonsmooth) minimization reformulations for it. We then discuss first-order methods suitable for solving these reformulations, namely, Nesterov’s optimal method [10, 11], Nesterov’s smooth ap ..."
Abstract
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Cited by 10 (1 self)
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In this paper we consider the general cone programming problem, and propose primal-dual convex (smooth and/or nonsmooth) minimization reformulations for it. We then discuss first-order methods suitable for solving these reformulations, namely, Nesterov’s optimal method [10, 11], Nesterov’s smooth
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