A new algorithm is proposed for solving large LMI feasibility problems, which exploits the structure of the LMI and avoids forming and manipulating large matrices. It is derived from the spectral bundle method of Helmberg and Rendl, but modified to properly handle inexact eigenvalues and eigenvectors obtained from Lanczos iterations. The complexity is estimated from numerical experiments and it...

The train timetabling problem considered is to find conflict free routes for a set of trains in a given railway network so that certain time window conditions are satisfied. We deal with the very large scale problem of constructing such timetables for the German railway network. A number of restrictions on different train types like freight trains or passenger trains have to be observed, e.g., ...

a gel composite (based on polyacrylamide and crosslinker cr(iii) acetate) was prepared by solvent method (distillate and water formation) and nanoclay particle (kaolinite). using xrd tests, d001 was evaluated for kaolinite nanoparticles in gel composite. kaolinite modification using dimethyl-sulfoxide led to increase interlamellar spacing from 7.21 to 10.82 o a. based on the results obtained fo...

This paper is to investigate the monotone variational inequalities (VIPs) in real Hilbert spaces. We constructed two iterative algorithms based on subgradient extragradient and Tseng?s for solving VIPs. Convergence analysis of suggested methods are proved. Several numerical examples illustrate efficiency given.

We propose a new algorithm for training a linear Support Vector Machine in the primal. The algorithm mixes ideas from non smooth optimization, subgradient methods, and cutting planes methods. This yields a fast algorithm that compares well to state of the art algorithms. It is proved to require O(1/λ ) iterations to converge to a solution with accuracy . Additionally we provide an exact shrinki...

The transmission rate, delivery reliability and network lifetime are three fundamental but conflicting design objectives in energy-constrained wireless sensor networks. In this paper, we address the optimal rate-reliability-lifetime tradeoff with link capacity constraint, reliability constraint and energy constraint. By introducing the weight parameters, we combine the objectives at rate, relia...

Boolean linear programs (BLPs) are ubiquitous in AI. Satisfiability testing, planning with resource constraints, and winner determination in combinatorial auctions are all examples of this type of problem. Although increasingly well-informed by work in OR, current AI research has tended to focus on specialized algorithms for each type of BLP task and has only loosely patterned new algorithms on...

We discuss a bundle method for non-smooth non-convex optimization programs. In the absence of convexity, a substitute for the cutting plane mechanism has to be found. We propose such a mechanism and prove convergence of our method in the sense that every accumulation point of the sequence of serious iterates is critical.

A level set method is proposed for solving free boundary problems coming from contact with obstacles. Two different approaches are described and applied for solving an unilateral obstacle problem. The cost functionals coming from the new approach are nonsmooth. For solving the nonsmooth minimization problems, two methods are applied: firstly, a proximal bundle method, which is a method for solv...