SUMMARYA new method for non-linear programming in general and structural optimization in particular is presented. In each step of the iterative process, a strictly convex approximating subproblem is generated and solved. The generation of these subproblems is controllcd by so called 'moving asymptotes', which may both stabilize and speed up the convergence of the general process.

Abstract. This paper deals with a certain class of optimization methods, based on conservative convex separable approximations (CCSA), for solving inequality-constrained nonlinear programming problems. Each generated iteration point is a feasible solution with lower objective value than the previous one, and it is proved that the sequence of iteration points converges toward the set of Karush-Kuhn-Tucker points. A major advantage of CCSA methods is that they can be applied to problems with a very large number of variables (say 10 4 -10 5 ) even if the Hessian matrices of the objective and constraint functions are dense.

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SUMMARYThis paper deals with topology optimization of discretized continuum structures. It is shown that a large class of non-linear 0-1 topology optimization problems, including stress-and displacement-constrained minimum weight problems, can equivalently be modelled as linear mixed 0-1 programs. The modelling approach is applied to some test problems which are solved to global optimality.