On the linearization of separable quadratic constraints in dual sequential convex programs

We study the replacement of dual subproblems based on separable quadratic objective and separable quadratic constraint functions by classical separable quadratic programs, in which the constraints are linearized. The quadratic subprograms are then solved in the dual space, which allows for a direct assessment of the computational implications that results from linearization of the separable quadratic constraints in the first place. The solution of the linearized QP forms in the dual space seems far easier than the solution of their quadratic–quadratic counterparts, which may have important implications for algorithms aimed at very large scale optimal design.

► We compare quadratic–linear subproblems to quadratic–quadratic subproblems.
► In structural optimization, quadratic–quadratic need not be more accurate.
► In addition, quadratic–linear may be easier to solve.
► Hence, quadratic–linear is attractive for very large scale optimization.
► Finally, for few constraints, pure dual QP statements may be desirable.