LINEARIZATION OF SECOND-ORDER CONE OPTIMIZATION PROBLEMS AND APPLICATION TO LIMIT ANALYSIS IN MECHANICAL ENGINEERING Convex optimization deals with a well-behaved subset of optimization problems that share nice properties, both from the theoretical (e.g. powerful duality theory) and the practical (existence of efficient algorithms) points of view. In the recent years, a lot of attention has been devoted to conic optimization, a reformulation of convex optimization based on the use of convex cones. Moreover, these problems can be solved in a polynomial number of iterations by a very efficient class of algorithms called interior-point methods (the analysis of these algorithms relies on the celebrated theory of self-concordant barriers from Nesterov and Nemirovsky). In particular, besides linear optimization, two subclasses of conic problems have been thoroughly studied within this framework: second-order optimization, a slight generalization of convex quadratic optimization and semidefinite optimization. In this talk, we focus on second-order cone optimization. Although dedicated solvers are commercially available, one often applies linearization schemes to these nonlinear problems. Moreover, besides the more or less trivial polyhedral approximation of a quadratic constraint, one can also use a clever linearization scheme proposed by Ben-Tal and Nemirovsky which basically allows an approximation with accuracy O(2^(-k)) using O(k) linear constraints and additional variables. One can then solve the resulting linear optimization problems using a standard interior-point algorithm. The purpose of the talk is to compare the application of these three different approaches to limit analysis, a class of problems arising in mechanical engineering that deals with the determination of the ruin load of a structure such as a metallic slab. We will outline the modelling of these problems as second-order cone optimization problems and present numerical results arising from computational experiments carried out with the different methods discussed above. Keywords: convex optimization, conic optimization, second-order cone optimization, linearization schemes ,limit analysis. - Y. Nesterov, A. Nemirovski, Interior-point Polynomial Algorithms in Convex Programming, SIAM, Philadelphia, 1994. - A. Ben-Tal, A. Nemirovski, Lectures on Modern Convex Optimization; Analysis, Algorithms, and Engineering Applications, MPS-SIAM series on Optimization, SIAM, Philadelphia, 2001. - A. Ben-Tal, A. Nemirovski, On Polyhedral Approximations of the Second-Order Cone, Mathematics of Operations Research, vol. 26 (2), May 2001, pp. 193--205.