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Constraint reduction for linear programs with many inequality constraints
 SIAM Journal on Optimization
, 2006
"... Consider solving a linear program in standard form, where the constraint matrix A is m × n, with n ≫ m ≫ 1. Such problems arise, for example, as the result of finely discretizing a semiinfinite program. The cost per iteration of typical primaldual interiorpoint methods on such problems is O(m 2 n) ..."
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Cited by 10 (4 self)
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Consider solving a linear program in standard form, where the constraint matrix A is m × n, with n ≫ m ≫ 1. Such problems arise, for example, as the result of finely discretizing a semiinfinite program. The cost per iteration of typical primaldual interiorpoint methods on such problems is O(m 2 n). We propose to reduce that
Features of similarity.
 Psychological Review
, 1977
"... Similarity plays a fundamental role in theories of knowledge and behavior. It serves as an organizing principle by which individuals classify objects, form concepts, and make generalizations. Indeed, the concept of similarity is ubiquitous in psychological theory. It underlies the accounts of stimu ..."
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Cited by 1455 (2 self)
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and metric assumptions are open to question. It has been argued by many authors that dimensional representations are appropriate for certain stimuli (e.g., colors, tones) but not for others. It seems more appropriate to represent faces, countries, or personalities in terms of many qualitative features than
Concentration Of Measure And Isoperimetric Inequalities In Product Spaces
, 1995
"... The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product# N of probability spaces has measure at least one half, "most" of the points of# N are "close" to A. We proceed to a systematic exploration of this phenomenon. The meaning o ..."
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Cited by 376 (4 self)
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of the word "most" is made rigorous by isoperimetrictype inequalities that bound the measure of the exceptional sets. The meaning of the work "close" is defined in three main ways, each of them giving rise to related, but different inequalities. The inequalities are all proved through a
Solving Existentially Quantified Constraints with One Equality and Arbitrarily Many Inequalities
 In Proc. of CP’03, LNCS 2833
, 2003
"... This paper contains the first algorithm that can solve disjunctions of constraints of the form g1 . . . ..."
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Cited by 6 (0 self)
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This paper contains the first algorithm that can solve disjunctions of constraints of the form g1 . . .
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 414 (21 self)
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We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization
Strictly Proper Scoring Rules, Prediction, and Estimation
, 2007
"... Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distribution F if he ..."
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Cited by 373 (28 self)
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scores. The continuous ranked probability score applies to probabilistic forecasts that take the form of predictive cumulative distribution functions. It generalizes the absolute error and forms a special case of a new and very general type of score, the energy score. Like many other scoring rules
CapitalSkill Complementarity and Inequality: A Macroeconomic Analysis
, 1997
"... There have been striking postwar changes in the supply and price of skilled labor relative to unskilled labor. The relative quantity of skilled labor has increased substantially, and the skill premium, which is the wage of skilled labor relative to unskilled labor, has grown significantly since 1980 ..."
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Cited by 289 (6 self)
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1980. Many studies have found that it is difficult to account for the increase in the skill premium on the basis of observable variables and have concluded that latent "skillbiased technological change" is the main factor responsible for the increase. This paper develops a framework
Cones of matrices and setfunctions and 01 optimization
 SIAM JOURNAL ON OPTIMIZATION
, 1991
"... It has been recognized recently that to represent a polyhedron as the projection of a higher dimensional, but simpler, polyhedron, is a powerful tool in polyhedral combinatorics. We develop a general method to construct higherdimensional polyhedra (or, in some cases, convex sets) whose projection a ..."
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Cited by 347 (7 self)
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of inequalities, such that already the first system includes clique, odd hole, odd antihole, wheel, and orthogonality constraints. In particular, for perfect (and many other) graphs, this first system gives the vertex packing polytope. For various classes of graphs, including tperfect graphs, it follows
c ○ 2006 Society for Industrial and Applied Mathematics CONSTRAINT REDUCTION FOR LINEAR PROGRAMS WITH MANY INEQUALITY CONSTRAINTS ∗
"... Abstract. Consider solving a linear program in standard form where the constraint matrix A is m × n, with n ≫ m ≫ 1. Such problems arise, for example, as the result of finely discretizing a semiinfinite program. The cost per iteration of typical primaldual interiorpoint methods on such problems i ..."
Abstract
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Abstract. Consider solving a linear program in standard form where the constraint matrix A is m × n, with n ≫ m ≫ 1. Such problems arise, for example, as the result of finely discretizing a semiinfinite program. The cost per iteration of typical primaldual interiorpoint methods on such problems is O(m2n). We propose to reduce that cost by replacing the normal equation matrix, AD2AT, where D is a diagonal matrix, with a “reduced ” version (of same dimension), AQD2 QAT Q, where Q is an index set including the indices of M most nearly active (or most violated) dual constraints at the current iterate, with M ≥ m a prescribed integer. This can result in a speedup of close to n/Q  at each iteration. Promising numerical results are reported for constraintreduced versions of a dualfeasible affinescaling algorithm and of Mehrotra’s predictorcorrector method [S. Mehrotra, SIAM J. Optim., 2 (1992), pp. 575–601]. In particular, while it could be expected that neglecting a large portion of the constraints, especially at early iterations, may result in a significant deterioration of the search direction, it appears that the total number of iterations typically remains essentially constant as the size of the reduced constraint set is decreased down to some threshold. In some cases this threshold is a small fraction of the total set. In the case of the affinescaling algorithm, global convergence and local quadratic convergence are proved.
The log of Gravity
 THE REVIEW OF ECONOMICS AND STATISTICS
, 2005
"... Although economists have long been aware of Jensen's inequality, many econometric applications have neglected an important implication of it: the standard practice of interpreting the parameters of loglinearized models estimated by ordinary least squares as elasticities can be highly misleadin ..."
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Cited by 333 (6 self)
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Although economists have long been aware of Jensen's inequality, many econometric applications have neglected an important implication of it: the standard practice of interpreting the parameters of loglinearized models estimated by ordinary least squares as elasticities can be highly
Results 1  10
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