Conservative approximations in nonlinear optimization. theory and examples

A new nonlinear optimization approach with strong convergence properties is presented. This approach is based on approximate subproblems, a nondifferentiable penalty function and a set active strategy, and is well suited for solution of design problems in engineering, where the number of variables may be large and function and gradient evaluations are very expensive (e.g. in structural optimization). The main theoretical results are presented, which lead to a general algorithm from which well-known methods (e.g. Pschenichny's baseline, method of hybrid approximations) can be seen as particular cases. Also, a new kind of convex approximation called SOC (second order correction) is introduced in this context, and some examples are solved by a practical algorithm implemented in a C module called ACPM.