We propose a family of search directions based on primal-dual entropy in the context of interior point methods for linear programming. This new family contains previously proposed search directions in the context of primal-dual entropy. We analyze the new family of search directions by studying their primal-dual affine-scaling and constant-gap centering components. We then design primal-dual in...

We discuss which are the main research themes in the field of search results clustering and report some recent results achieved by the Information Mining group at Fondazione Ugo Bordoni.

-----------------------------The efficient combination of directions is a significant problem in line search methods that either use negative curvature. or wish to include additional information such as the gradient or different approximations to the Newton direction. In thls paper we describe a new procedure to combine several of these directions within an interior-point primal-dual algorithm....

Two nonsymmetric search directions for semideenite programming, the XZ and ZX search directions, are proposed. They are derived from a nonsymmetric formulation of the semideenite programming problem. The XZ direction corresponds to the direct linearization of the central path equation XZ = I; while the ZX direction corresponds to ZX = I. The XZ and ZX directions are well deened if both X and Z ...

Keeping track of scientific challenges, advances and emerging directions is a fundamental part research. However, researchers face flood papers that hinders discovery important knowledge. In biomedicine, this directly impacts human lives. To address problem, we present novel task extraction search challenges directions, to facilitate rapid knowledge discovery. We construct release an expert-ann...

In this paper two simple examples of a twice continuously differentiable strictly convex function f are presented for which Newton’s method with line search converges to a point where the gradient of f is not zero. The first example uses a line search based on the Wolfe conditions. For the second example, some strictly convex function f is defined as well as a sequence of descent directions for...

A tolerant derivative–free nonmonotone line search technique is proposed and analyzed. Several consecutive increases in the objective function and also non descent directions are admitted for unconstrained minimization. To exemplify the power of this new line search we describe a direct search algorithm in which the directions are chosen randomly. The convergence properties of this random metho...