Confidence Single-Level Formulation in Structural Robust Optimization and its Solution Aspect

Structural robust optimization problems are often solved via the so-called Bi-level approach. The solution of Bi-level optimization problems often involves large computational efforts and sometimes the convergence behavior is not so good because of the non-smooth nature of the Bi-level formulation. In the present paper, confidence single-level nonlinear semi-definite programming (NLSDP) formulations for structural robust optimization problems under stiffness uncertainties are proposed. This is achieved by using some technical tools such as S-procedure and quadratic embedding in convex analysis. The resulting NLSDP problems are then solved using Augmented Lagrange Multiplier Method with sound mathematical properties. Furthermore, the deficiencies of the naive single level formulation in literatures are also analyzed. Numerical examples show that confidence robust optimal solutions can be obtained with the proposed approach effectively.

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