One revisits the standard saddle-point method based on conjugate duality for solving convex minimization problems. Our aim is to reduce or remove unnecessary topological restrictions on the constraint set. Dual equalities and characterizations of the minimizers are obtained with weak or without constraint qualifications. The main idea is to work with intrinsic topologies which reflect some geom...

we introduce variational inequality problems on hilbert $c^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. then relation between variational inequalities, $c^*$-valued metric projection and fixed point theory  on  hilbert $c^*$-modules is studied.

Minimization of the L∞ norm, which can be viewed as approximately solving the non-convex least median estimation problem, is a powerful method for outlier removal and hence robust regression. However, current techniques for solving the problem at the heart of L∞ norm minimization are slow, and therefore cannot scale to large problems. A new method for the minimization of the L∞ norm is presente...

To the moment we have more or less complete impression of what is the complexity of solving general nonsmooth convex optimization problems and what are the corresponding optimal methods. In this lecture we treat a new topic: optimal methods for smooth convex minimization. We shall start with the simplest case of unconstrained problems with smooth convex objective. Thus, we shall be interested i...

This paper deals with iterative gradient and subgradient methods with random feasibility steps for solving constrained convex minimization problems, where the constraint set is specified as the intersection of possibly infinitely many constraint sets. Each constraint set is assumed to be given as a level set of a convex but not necessarily differentiable function. The proposed algorithms are ap...

In this paper, we propose an algorithm for computing the farthest-segment Voronoi diagram for the edges of a convex polygon and apply this to obtain an O(n logn) algorithm for the following proximity problem: Given a set P of n (>2) points in the plane, we have O(n2) implicitly defined segments on pairs of points. For each point p ∈ P , find a segment from this set of implicitly defined segment...

APPLYING CONVEX OPTIMIZATION TECHNIQUES TO ENERGY MINIMIZATION PROBLEMS IN COMPUTER VISION Arvind Bhusnurmath C.J.Taylor Energy minimization is an important technique in computer vision that has been applied to practically all early vision problems. Several methods have been proposed to solve the problem and to date, the most popular ones have been discrete optimization approaches such as graph...