Automated software refactoring is known to be one of the "hard" combinatorial optimization problems of the search-based software engineering field. The difficulty is mainly due to candidate solution representation, objective function description and necessity of functional behavior preservation of software. The problem is formulated as a combinatorial optimization problem whose objective functi...

Among the compact homogeneous spaces, a very distinguished subclass is formed by the (generalized) real flag manifolds which by definition are the orbits of the isotropy representations of Riemannian symmetric spaces (sorbits). This class contains most compact symmetric spaces (e.g. all hermitian ones), all classical flag manifolds over real, complex and quaternionic vector spaces, all adjoint ...

The watershed transform is a powerful and popular tool for segmenting objects whose contours appear as crest lines on a gradient image : it associates to a topographic surface a partition into catchment basins, defined as attraction zones of a drop of water falling on the relief and following a line of steepest descent. To each regional minimum corresponds a catchment basin. Points from where s...

In recent years it has been made more and more clear that the critical issue in gradient methods is the choice of the step length, whereas using the gradient as search direction may lead to very effective algorithms, whose surprising behaviour has been only partially explained, mostly in terms of the spectrum of the Hessian matrix. On the other hand, the convergence of the classical Cauchy stee...

Many structured large-scale linear programming problems can be transformed into an equivalent problem of maximizing a piecewise linear, concave function subject to linear constraints. The equivalent problem can, in turn, be solved in a finite number of steps using a steepest ascent algorithm. This principle is applied to block diagonal systems yielding refinements of existing algorithms. An app...

For p 2 (1; 1) and n > 0 we consider the scalar doubly degenerate diiusion equation @ t s ? div(jrs n j p?2 rs n) = 0 in (0; 1) (1) with no{{ux boundary conditions. We argue that this evolution problem can be understood as steepest descent of the convex functional sign(m ? 1) Z s m ; provided m := n + p ? 2 p ? 1 > 0 ; (2) w. r. t. the Wasserstein metric of order p on the space of probability d...

We consider the special case of the restarted Arnoldi method for approximating the product of a function of a Hermitian matrix with a vector which results when the restart length is set to one. When applied to the solution of a linear system of equations, this approach coincides with the method of steepest descent. We show that the method is equivalent with an interpolation process in which the...

A generalization of the steepest descent and other methods for solving a large scale symmetric positive definitive system Ax = b is presented. Given a positive integer m, the new iteration is given by xk+1 = xk −λ(xν(k))(Axk − b), where λ(xν(k)) is the steepest descent step at a previous iteration ν(k) ∈ {k, k−1, . . . , max{0, k−m}}. The global convergence to the solution of the problem is est...