An improved generalized inverse algorithm for linear inequalities and its applications

Iterative, two-class algorithm for linear inequalitie

5 Post-processing methods for passivity enforcement

Many physical systems are passive (or dissipative): they are unable to generate energy on their own, but they can store energy in some form while exchanging power with the surrounding environment. This chapter describes the most prominent approaches for ensuring that Reduced Order Models are passive, so that their math- ematical representation satisfies an appropriate dissipativity condition. The main focus is on Linear and Time-Invariant (LTI) systems in state-space form. Different conditions for testing passivity of a given LTI model are discussed, including Linear Matrix Inequalities (LMIs), Frequency-Domain Inequalities, and spectral conditions on associated Hamiltonian matrices. Then we describe common approaches for perturbing a given non-passive system to enforce its passivity. Various examples from electronic applications are used to demonstrate both theory and algorithm performance

Linearly Convergent First-Order Algorithms for Semi-definite Programming

In this paper, we consider two formulations for Linear Matrix Inequalities (LMIs) under Slater type constraint qualification assumption, namely, SDP smooth and non-smooth formulations. We also propose two first-order linearly convergent algorithms for solving these formulations. Moreover, we introduce a bundle-level method which converges linearly uniformly for both smooth and non-smooth problems and does not require any smoothness information. The convergence properties of these algorithms are also discussed. Finally, we consider a special case of LMIs, linear system of inequalities, and show that a linearly convergent algorithm can be obtained under a weaker assumption

The STRESS Method for Boundary-point Performance Analysis of End-to-end Multicast Timer-Suppression Mechanisms

Evaluation of Internet protocols usually uses random scenarios or scenarios based on designers' intuition. Such approach may be useful for average-case analysis but does not cover boundary-point (worst or best-case) scenarios. To synthesize boundary-point scenarios a more systematic approach is needed.In this paper, we present a method for automatic synthesis of worst and best case scenarios for protocol boundary-point evaluation. Our method uses a fault-oriented test generation (FOTG) algorithm for searching the protocol and system state space to synthesize these scenarios. The algorithm is based on a global finite state machine (FSM) model. We extend the algorithm with timing semantics to handle end-to-end delays and address performance criteria. We introduce the notion of a virtual LAN to represent delays of the underlying multicast distribution tree. The algorithms used in our method utilize implicit backward search using branch and bound techniques and start from given target events. This aims to reduce the search complexity drastically. As a case study, we use our method to evaluate variants of the timer suppression mechanism, used in various multicast protocols, with respect to two performance criteria: overhead of response messages and response time. Simulation results for reliable multicast protocols show that our method provides a scalable way for synthesizing worst-case scenarios automatically. Results obtained using stress scenarios differ dramatically from those obtained through average-case analyses. We hope for our method to serve as a model for applying systematic scenario generation to other multicast protocols.Comment: 24 pages, 10 figures, IEEE/ACM Transactions on Networking (ToN) [To appear

The Metric Nearness Problem

Metric nearness refers to the problem of optimally restoring metric properties to distance measurements that happen to be nonmetric due to measurement errors or otherwise. Metric data can be important in various settings, for example, in clustering, classification, metric-based indexing, query processing, and graph theoretic approximation algorithms. This paper formulates and solves the metric nearness problem: Given a set of pairwise dissimilarities, find a “nearest” set of distances that satisfy the properties of a metric—principally the triangle inequality. For solving this problem, the paper develops efficient triangle fixing algorithms that are based on an iterative projection method. An intriguing aspect of the metric nearness problem is that a special case turns out to be equivalent to the all pairs shortest paths problem. The paper exploits this equivalence and develops a new algorithm for the latter problem using a primal-dual method. Applications to graph clustering are provided as an illustration. We include experiments that demonstrate the computational superiority of triangle fixing over general purpose convex programming software. Finally, we conclude by suggesting various useful extensions and generalizations to metric nearness