If a strong suucient optimality condition of second order together with the Mangasarian-Fromowitz and the constant rank constraint quali-cations are satissed for a parametric optimization problem, then a local optimal solution is strongly stable in the sense of Kojima and the corresponding optimal solution function is locally Lipschitz continuous. In the article the possibilities for the comput...

Many structured prediction tasks involve complex models where inference is computationally intractable, but where it can be well approximated using a linear programming relaxation. Previous approaches for learning for structured prediction (e.g., cuttingplane, subgradient methods, perceptron) repeatedly make predictions for some of the data points. These approaches are computationally demanding...

This paper considers a distributed constrained optimization problem, where the objective function is the sum of local objective functions of distributed nodes in a network. The estimate of each agent is restricted to different convex sets. To solve this optimization problem which is not necessarily smooth, we study a novel distributed projected subgradient algorithm for multi-agent optimization...

Two heuristics for the Linear Ordering Problem are investigated in this paper. heuristics are embedded within a Lagrangian Relaxation framework and are initiated with a construction phase. In this process, some Lagrangian (dual) information is used as an input to guide the construction of initial Linear Orderings. Solutions thus obtained are then submitted to local improvement in an overall pro...

A subdifferentiable global contact detection algorithm, the Supporting Separating Hyperplane (SSH) algorithm, based on the signed distance between supporting hyperplanes of two convex sets is developed. It is shown that for polyhedral sets, the SSH algorithm may be evaluated as a linear program, and that this linear program is always feasible and always subdifferentiable with respect to the con...

In this paper we investigate an approach to provide approximate, anytime algorithms for DCOPs that can provide quality guarantees. At this aim, we propose the divide-and-coordinate (DaC) approach. Such approach amounts to solving a DCOP by iterating (1) a divide stage in which agents divide the DCOP into a set of simpler local subproblems and solve them; and (2) a coordinate stage in which agen...

We study the subgradient projection method for convex optimization with Brr ann-lund's level control for estimating the optimal value. We establish global convergence in objective values without additional assumptions employed in the literature.

For solving non-smooth multidimensional optimization problems, we present a family of relaxation subgradient methods (RSMs) with built-in algorithm for finding the descent direction that forms an acute angle all subgradients in neighborhood current minimum. Minimizing function along opposite (with minus sign) enables to go beyond The algorithms is based on systems inequalities. finite convergen...