TY - JOUR

T1 - Conservative approximations in nonlinear optimization. theory and examples

AU - Longo, A.

AU - Nó, M.

AU - Aizpitarte, M.

AU - Unzueta, J.

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0025745651&partnerID=8YFLogxK

U2 - 10.1016/0045-7949(91)90052-N

DO - 10.1016/0045-7949(91)90052-N

M3 - Article

AN - SCOPUS:0025745651

SN - 0045-7949

VL - 39

SP - 441

EP - 449

JO - Computers and Structures

JF - Computers and Structures

IS - 5

ER -