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A new algorithm for unconstrained optimization is presented which is based on a modified one-dimensional bisection method. The algorithm actually uses only the signs of function and gradient values. Thus it can be applied to problems with imprecise function and gradient values. It converges in one iteration on quadratic functions of n variables, it rapidly… (More)

In this paper we present a new algorithm for finding the unconstrained minimum of a continuously differentiable function f (x) in n variables. This algorithm is based on a conic model function, which does not involve the conjugacy matrix or the Hessian of the model function. The conic method in this paper is combined with a non-monotone line search using… (More)

2 3 −approximation matching algorithm is sub-exponential. Abstract Manne et al. [11] designed the first algorithm computing a maximal matching that is a 2 3-approximation of the maximum matching in 2 O(n) moves. However, the complexity tightness was not proved. In this paper, we exhibit a sub-exponential execution of this matching algorithm : this algorithm… (More)

In this paper we present a new algorithm for finding the unconstrained minimum of a twice–continuously differentiable function f (x) in n variables. This algorithm is based on a conic model function, which does not involve the conjugacy matrix or the Hessian of the model function. The basic idea in this paper is to accelerate the convergence of the conic… (More)

We present the first polynomial self-stabilizing algorithm for finding a 2 3-approximation of a maximum matching in a general graph. The previous best known algorithm has been presented by Manne et al. [6] and has a sub-exponential time complexity under the distributed adversarial daemon [1]. Our new algorithm is an adaptation of the Manne et al. algorithm… (More)

Del Pia and Michini recently improved the upper bound of kd due to Klein-schmidt and Onn for the largest possible diameter of the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. We introduce Euler polytopes which include a family of lattice polytopes with diameter (k + 1)d/2, and thus reduce the gap between the… (More)

A graph is k-degenerate if any induced subgraph has a vertex of degree at most k. In this paper we prove new algorithms finding cliques and similar structures in these graphs. We design linear time Fixed-Parameter Tractable algorithms for induced and non induced bicliques. We prove an algorithm listing all maximal bicliques in time O(k 3 (n − k)2 k),… (More)

A graph is inductive k-independent if there exists an ordering of its vertices v1, ..., vn such that α(G[N (vi)∩Vi]) ≤ k where N (vi) is the neighbourhood of vi, Vi = {vi, ..., vn} and α is the independence number. In this article we design a polynomial time approximation algorithm with ratio ∆/ log(log(∆)/(k + 1)) for the maximum clique problem and also… (More)

In a recent article, we introduced a method based on a conic model for unconstrained optimization. The acceleration of the convergence of this method was obtained by choosing more appropriate points in order to apply the conic model. In particular, we applied in the gradient of the objective function a dimension-reducing method for the numerical solution of… (More)

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