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Several formulations are known for robust compliance optimization of structures subjected to uncertain static external loads. Aiming at providing clear perspective of the problem, this paper establishes connection between three formulations: a semidefinite programming formulation, a formulation as minimization of the maximum eigenvalue of a symmetric matrix, and a formulation using a generalized eigenvalue problem. Equivalence of these formulations is shown by using a fundamental property of the Schur complement of a symmetric positive semidefinite matrix. A series of numerical examples is presented to show that an optimal solution of the robust compliance optimization problem can possibly have eigenvalues of large multiplicity.

A NOTE ON FORMULATIONS OF ROBUST COMPLIANCE OPTIMIZATION UNDER UNCERTAIN LOADS