Real-life dynamic problems may lead to inconsistent constraints systems for which a solution must be found even if constraints have to be relaxed. In this paper, we propose a bestrst search to handle such problems. Classical backtracking search algorithms are extended in two ways: identi cation of good backtrack points as in Intelligent Backtracking techniques and maximum use of independant wor...

In the field of Ramsey theory, the weak Schur number WS(k) is the largest integer n for which their exists a partition into k subsets of the integers [1, n] such that there is no x < y < z all in the same subset with x+y = z. Although studied since 1941, only the weak Schur numbersWS(1) throughWS(4) are precisely known, for k ≥ 5 theWS(k) are only bracketed within rather loose bounds. We tackle...

The purpose of this study is to research how Chinese university students solve information-based problems. With the Search Performance Index as the measure of search success, participants were divided into high, medium and low-performing groups. Based on their web search logs, these three groups were compared along five dimensions of the search process for answers to the assigned tasks: frequen...

In recent years, many improvements to backtracking algorithms for solving constraint satisfaction problems have been proposed. The techniques for improving backtracking algorithms can be conveniently classiied as look-ahead schemes and look-back schemes. Unfortunately , look-ahead and look-back schemes are not entirely orthogonal as it has been observed empirically that the enhancement of look-...

In this paper a second-order method for solving large-scale strongly convex `1-regularized problems is developed. The proposed method is a NewtonCG (Conjugate Gradients) algorithm with backtracking line-search embedded in a doubly-continuation scheme. Worst-case iteration complexity of the proposed Newton-CG is established. Based on the analysis of Newton-CG, worstcase iteration complexity of t...

This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with Hölder continuous gradients. The proposed schemes are optimal for smooth strongly convex problems with Lipschitz continuous gradients and optimal up to a logarithmic fac...

Binary classification is the problem of predicting the class a given sample belongs to. To achieve a good prediction performance, it is important to find a suitable model for a given dataset. However, it is often time consuming and impractical for practitioners to try various classification models because each model employs a different formulation and algorithm. The difficulty can be mitigated ...

Linear SVMs are a popular choice of binary classifier. It is often necessary to train many different classifiers on a multiclass dataset in a one-versus-rest fashion, and this for several values of the regularization constant. We propose to harness GPU parallelism by training as many classifiers as possible at the same time. We optimize the primal L2-loss SVM objective using the conjugate gradi...

This paper derives upper bounds on the expected number of search tree nodes visited during an m-solution backtracking search, a search which terminates after some pre-selected number m problem solutions are found. The search behavior is assumed to have a general probabilistic structure. Our results are stated in terms of node expansion and contraction. A visited search tree node is said to be e...

In this paper, we investigate a linearized proximal algorithm (LPA) for solving a convex composite optimization problem. Each iteration of the LPA is a proximal minimization on the composition of the outer function and the linearization of the inner function at current iterate. The LPA has the attractive computational advantage that the solution of each subproblem is a singleton, which avoids t...