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.