First we give a short description of the Extended Linear Complementarity Problem (ELCP), which is a mathematical programming problem. We brieey discuss how this problem can be used in the analysis of discrete event systems and continuous variable systems. Next we show that the ELCP can also be used to model and to analyze hybrid systems. More speciically, we consider a traac-light-controlled in...

1 Overview We had a general overview of semidefinite programming(SDP) in lecture 1, starting from this lecture we will be jumping into the theory. Some topics we will discuss in the next few lectures include: the duality theory, notion of complementary slackness, at least one polynomial time algorithm of solving SDP and application in integer programming and combinatorial optimization. Througho...

Esophagitis is a condition of inflammation of the esophageal mucosa, which is also called as acid reflux disease. The cause maybe be due to slackness of the lower esophageal sphintcer which allows acidic contents of the food from stomach to esophagus. Esophagitis is detected by observing the esophagus by video endoscopy of the Upper Gastro-Intestinal tract. The classification of esophagitis is ...

In this paper we present linear time approximation schemes for several generalized matching problems on nonbipartite graphs. Our results include O (m)-time algorithms for (1 − )maximum weight f -factor and (1+ )-approximate minimum weight f -edge cover. As a byproduct, we also obtain direct algorithms for the exact cardinality versions of these problems running in O(m √ f(V )) time. The technic...

The primal-dual method (or primal-dual schema) is another means of solving linear programs. The basic idea of this method is to start from a feasible solution y to the dual program, then attempt to find a feasible solution x to the primal program that satisfies the complementary slackness conditions. If such an x cannot be found, it turns out that we can find a better y in terms of its objectiv...

Providing an analytical solution for the problem of finding Fastest Distributed Consensus (FDC) is one of the challenging problems in the field of sensor networks. Here in this work we present analytical solution for the problem of fastest distributed consensus averaging algorithm by means of stratification and semi-definite programming, for two particular types of Petal networks, namely symmet...

We define the total weak discrepancy of a poset P as the minimum nonnegative integer k for which there exists a function f : V → Z satisfying (i) if a ≺ b then f(a) + 1 ≤ f(b) and (ii) ∑ |f(a)− f(b)| ≤ k, where the sum is taken over all unordered pairs {a, b} of incomparable elements. If we allow k and f to take real values, we call the minimum k the fractional total weak discrepancy of P . The...

Electrodynamic tethers can be employed as an immensely promising propulsion system for boosting the altitude of spacecraft, cite instance space stations, satellites, and like, which ameliorates expenditure fuel minimizes detrimental spacecraft impacts. This paper analyzes libration dynamics stability reboost with insulation electrodynamic tethers. A key aspect tether is how to keep aligned loca...

We consider nonlinear programs with inequality constraints, and we focus on the problem of identifying those constraints which will be active at an isolated local solution. The correct identification of active constraints is important from both a theoretical and a practical point of view. Such an identification removes the combinatorial aspect of the problem and locally reduces the inequality c...