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s of the Presentations Solving inconsistencys preserving the zero-structure Paula Amaral, Joaquim Júdice and Hanif Sherali, University of Coimbra In this talk we describe an nonlinear optimization model for correcting an inconsistent linear system. By correction we mean a perturbation of both the matrix of coefficients and right-hand-side of the linear system of inequalities. Inconsistency of a linear model arises in many practical applications. Two global optimization approaches for solving this non-convex nonlinear problem are presented. One algorithm uses a linearization approach while the second algorithm exploits Reformulation-Linearization techniques (RLT). E-mail: [email protected] , [email protected] A Semidefinite Optimization Approach for Single Row Layout Problems Miguel F. Anjos, University of Waterloo The row layout problem is concerned with finding optimal linear placements of facilities with varying dimensions. This problem occurs in a number of industrial contexts, such as the layout of goods in a warehouse and the layout of machines on a factory floor. It is closely related to the linear ordering problem, which also has a number of practical applications. Most versions of this problem are known to be NP-hard, and previous globally optimal approaches are ineffective on problems with 20 or more facilities. We propose a semidefinite programming formulation which provides the first non-trivial global lower bounds for large instances of this problem. The formulation captures the natural symmetry of the problem and does not require symmetrybreaking constraints. Furthermore, applying simple heuristic procedures to the