First‐order sequential convex programming using approximate diagonal QP subproblems

Optimization algorithms based on convex separable approximations for optimal structural design often use reciprocal‐like approximations in a dual setting; CONLIN and the method of moving asymptotes (MMA) are well‐known examples of such sequential convex programming (SCP) algorithms. We have previously demonstrated that replacement of these nonlinear (reciprocal) approximations by their own second order Taylor series expansion provides a powerful new algorithmic option within the SCP class of algorithms. This note shows that the quadratic treatment of the original nonlinear approximations also enables the restatement of the SCP as a series of Lagrange‐Newton QP subproblems. This results in a diagonal trust‐region SQP type of algorithm, in which the second order diagonal terms are estimated from the nonlinear (reciprocal) intervening variables, rather than from historic information using an exact or a quasi‐Newton Hessian approach. The QP formulation seems particularly attractive for problems with far more constraints than variables (when pure dual methods are at a disadvantage), or when both the number of design variables and the number of (active) constraints is very large.