Rahul Mehrotra is an architect , urban designer and principal with Rahu/ Mehrotra Associates, Bombay,/ndia. He has a Master 's degree in Urban Design from Harvard University. He is Executive Director of the Urban Design Research Institute, and on the Board of Governors of the Mumbai Metropolitan Regional Development Authority's Heritage Society. Recent books include, Bombay-The Cities Within, a...

Ariyawansa and Zhu [5] have recently proposed a new class of optimization problems termed stochastic semidefinite programs (SSDP’s). SSDP’s may be viewed as an extension of two-stage stochastic (linear) programs with recourse (SLP’s). Zhao [25] has derived a decomposition algorithm for SLP’s based on a logarithmic barrier and proved its polynomial complexity. Mehrotra and Özevin [17] have exten...

The best method known for determining lower bounds on the vertex coloring number of a graph is the linear-programming column-generation technique, where variables correspond to stable sets, first employed by Mehrotra and Trick in 1996. We present an implementation of the method that provides numerically-safe results, independent of the floating-point accuracy of linear-programming software. Our...

Abstract A new primal-dual interior-point algorithm applicable to nonsymmetric conic optimization is proposed. It a generalization of the famous suggested by Nesterov and Todd for symmetric case, uses scalings cones proposed Tunçel. We specialize Tunçel’s important case 3 dimensional exponential-cones, resulting in practical with good numerical performance, on level standard cone ( e.g. , quadr...

Automated inspection of Printed Circuit Boards(PCB's) is essential if 100% repeatible inspection is to be carried out. The cost of most commercially available systems for automatic visual inspection of PCB's are beyond the reach of many small to medium manufacturers. The principle objectives of our research is to develop and integrate a micro-computer based image analysis system specifically fo...

The problem of minimizing a sum of Euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature. This nonsmooth optimization problem arises in many different kinds of modern scientific applications. We derive a primal-dual interior-point algorithm for the problem, by applying Newton’s method directly to a system of nonlinear e...

Primal-dual path-following algorithms are considered for determinant maximization problem (maxdet-problem). These algorithms apply Newton's method to a primal-dual central path equation similar to that in semideenite programming (SDP) to obtain a Newton system which is then symmetrized to avoid nonsymmetric search direction. Computational aspects of the algorithms are discussed, including Mehro...

Two nonsymmetric search directions for semideenite programming, the XZ and ZX search directions, are proposed. They are derived from a nonsymmetric formulation of the semideenite programming problem. The XZ direction corresponds to the direct linearization of the central path equation XZ = I; while the ZX direction corresponds to ZX = I. The XZ and ZX directions are well deened if both X and Z ...