3 Convex functions on symmetric spaces 11 3.1 Geometric preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.1 Metric spaces with curvature bounds . . . . . . . . . . . . . . 11 3.1.2 Hadamard spaces . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.3 Symmetric spaces of noncompact type . . . . . . . . . . . . . 15 3.1.4 Auxiliary results . . . . . . . . . . . . . . . ....

We present a version of the gravitational method for linear programming, based on steepest descent gravitational directions. Finding the direction involves a special small “nearest point problem” that we solve using an efficient geometric approach. The method requires no expensive initialization, and operates only with a small subset of locally active constraints at each step. Redundant constra...

A new smoothing algorithm for the solution of nonlinear complementarity problems (NCP) is introduced in this paper. It is based on semismooth equation reformulation of NCP by Fischer–Burmeister function and its related smooth approximation. In each iteration the corresponding linear system is solved only approximately. Since inexact directions are not necessarily descent, a nonmonotone techniqu...

In two recent papers regularization methods based on Taylor polynomial models for minimization were proposed that only rely on Hölder conditions on the higher order employed derivatives. Grapiglia and Nesterov considered cubic regularization with a sufficient descent condition that uses the current gradient and resembles the classical Armijo’s criterion. Cartis, Gould, and Toint used Taylor mod...

In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdir...

Abstract. We extend Stanley’s work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting permutations we study their generating polynomials by number of excedances. Several techniques are used: Désarménien’s desarrangement combinatorics, Ge...

Recent works in the nonlinear MPC literature have presented “realtime” optimization approaches based upon incremental updating of input parameters using local descent directions of the cost functional. The main downside to these methods is their strong dependence upon the values used to initialize the input parameters. In this note we study the robustness issues associated with nonlocal search ...

background: in most of defecography films, the symphysis pubis is obscured, especially in obese patients, and the parameters will change in values if x-ray is interpreted by different reviewers or if the patient changes his/her position between the phases. this study was carried out to determine how to do the defecography to obtain fixed parameters. â  methods: eighty patients that had been can...