### Uittreksel

Taal | Engels |
---|---|

Pagina's | 479-488 |

Aantal pagina's | 10 |

Tijdschrift | Structural and Multidisciplinary Optimization |

Volume | 45 |

Nummer van het tijdschrift | 4 |

DOI's | |

Status | Gepubliceerd - 2012 |

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### Citeer dit

*Structural and Multidisciplinary Optimization*,

*45*(4), 479-488. DOI: 10.1007/s00158-011-0739-3

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*Structural and Multidisciplinary Optimization*, vol. 45, nr. 4, blz. 479-488. DOI: 10.1007/s00158-011-0739-3

**First-order sequential convex programming using approximate diagonal QP subproblems.** / Etman, L.F.P.; Groenwold, A.A.; Rooda, J.E.

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

TY - JOUR

T1 - First-order sequential convex programming using approximate diagonal QP subproblems

AU - Etman,L.F.P.

AU - Groenwold,A.A.

AU - Rooda,J.E.

PY - 2012

Y1 - 2012

N2 - Optimization algorithms based on convex separable approximations for optimal structural design often use reciprocal-like approximations in a dual setting; CONLIN and the method of moving asymptotes (MMA) are well-known examples of such sequential convex programming (SCP) algorithms. We have previously demonstrated that replacement of these nonlinear (reciprocal) approximations by their own second order Taylor series expansion provides a powerful new algorithmic option within the SCP class of algorithms. This note shows that the quadratic treatment of the original nonlinear approximations also enables the restatement of the SCP as a series of Lagrange-Newton QP subproblems. This results in a diagonal trust-region SQP type of algorithm, in which the second order diagonal terms are estimated from the nonlinear (reciprocal) intervening variables, rather than from historic information using an exact or a quasi-Newton Hessian approach. The QP formulation seems particularly attractive for problems with far more constraints than variables (when pure dual methods are at a disadvantage), or when both the number of design variables and the number of (active) constraints is very large.

AB - Optimization algorithms based on convex separable approximations for optimal structural design often use reciprocal-like approximations in a dual setting; CONLIN and the method of moving asymptotes (MMA) are well-known examples of such sequential convex programming (SCP) algorithms. We have previously demonstrated that replacement of these nonlinear (reciprocal) approximations by their own second order Taylor series expansion provides a powerful new algorithmic option within the SCP class of algorithms. This note shows that the quadratic treatment of the original nonlinear approximations also enables the restatement of the SCP as a series of Lagrange-Newton QP subproblems. This results in a diagonal trust-region SQP type of algorithm, in which the second order diagonal terms are estimated from the nonlinear (reciprocal) intervening variables, rather than from historic information using an exact or a quasi-Newton Hessian approach. The QP formulation seems particularly attractive for problems with far more constraints than variables (when pure dual methods are at a disadvantage), or when both the number of design variables and the number of (active) constraints is very large.

U2 - 10.1007/s00158-011-0739-3

DO - 10.1007/s00158-011-0739-3

M3 - Article

VL - 45

SP - 479

EP - 488

JO - Structural and Multidisciplinary Optimization

T2 - Structural and Multidisciplinary Optimization

JF - Structural and Multidisciplinary Optimization

SN - 1615-147X

IS - 4

ER -