Positive definite separable quadratic programs for non-convex problems

We propose to enforce positive definiteness of the Hessian matrix in a sequence of separable quadratic programs, without demanding that the individual contributions from the objective and the constraint functions are all positive definite. For problems characterized by non-convex objective or constraint functions, this may result in a notable computational advantage. Even though separable quadratic programs are of interest in their own right, they are of particular interest in structural optimization, due to the so-called ‘approximated-approximations’ approach. This approach allows for the construction of quadratic approximations to the reciprocal-like approximations used, for example, in CONLIN and MMA. To demonstrate some of the ideas proposed, the optimal topology design of a structure subject to local stress constraints is studied as one of the examples.