Numerical experiences show that bundle methods are very efficient for solving convex non-smooth optimization problems. In this paper we describe briefly the mathematical background of a bundle method and discuss practical aspects for the numerical implementation. Further, we give a detailed documentation of our implementation and report about numerical tests.

The hierarchical edge bundle method clusters the edges of a radial layout to better understand and analyze graphs, but its effectiveness relies critically on the quality of the hierarchical organization of its nodes and edges. This paper proposes a novel graph visualization approach that extracts the community structure of a network and organizes it into a more balanced and meaningful hierarchy...

We present here an alternative method for calculating magnifications in gravitational lensing calculations – the Ray Bundle method. We provide a detailed comparison between the distribution of magnifications obtained compared with analytic results and conventional ray-shooting methods. The Ray Bundle method provides high accuracy in the weak lensing limit, and is computationally much faster tha...

In this paper we propose a strongly convergent variant on the projected subgradient method for constrained convex minimization problems in Hilbert spaces. The advantage of the proposed method is that it converges strongly when the problem has solutions, without additional assumptions. The method also has the following desirable property: the sequence converges to the solution of the problem whi...

We describe an approach to the parallel and distributed solution of large-scale, block structured semidefinite programs using the spectral bundle method. Various elements of this approach (such as data distribution, an implicitly restarted Lanczos method tailored to handle block diagonal structure, a mixed polyhedralsemidefinite subdifferential model, and other aspects related to parallelism) a...

The last few years have seen the advent of a new generation of bundle methods, capable to handle inexact oracles, polluted by “noise”. Proving convergence of a bundle method is never simple and coping with inexact oracles substantially increases the technicalities. Besides, several variants exist to deal with noise, each one needing an ad hoc proof to show convergence. We state a synthetic conv...

This work presents Lagrangean/surrogate relaxation to the problem of maximum pro®t assignment of n tasks to m agents (n > m), such that each task is assigned to only one agent subject to capacity constraints on the agents. The Lagrangean/surrogate relaxation combines usual Lagrangean and surrogate relaxations relaxing ®rst a set of constraints in the surrogate way. Then, the Lagrangean relaxati...

A projected subgradient method for solving a class of set-valued mixed variational inequalities (SMVIs) is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.

Vibrotactile stimulation system that generates haptic illusion by employing a RA mechanoreceptor model is developed. The developed stimulator consists of an array of 6 by 4 tiny ultrasonic linear motors [1, 2] with nominal pitch of 2.9mm. Distal pad of human finger with RA mechanoreceptors is modeled using Bensmaia’s RA model [3]. In addition, stimulation characteristics of the motor are calibr...