First-order sequential convex programming using approximate diagonal QP subproblems

L.F.P. Etman, A.A. Groenwold, J.E. Rooda

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

21 Citaties (Scopus)

Uittreksel

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.
TaalEngels
Pagina's479-488
Aantal pagina's10
TijdschriftStructural and Multidisciplinary Optimization
Volume45
Nummer van het tijdschrift4
DOI's
StatusGepubliceerd - 2012

Vingerafdruk

Convex optimization
Convex Programming
First-order
Approximation
Asymptote
Dual Method
Nonlinear Approximation
Quasi-Newton
Trust Region
Taylor Series Expansion
Structural Design
Lagrange
Replacement
Taylor series
Optimization Algorithm
Structural design
Series
Formulation
Term

Citeer dit

@article{5aa4085bfd5e4d5b868e37ce1b73db28,
title = "First-order sequential convex programming using approximate diagonal QP subproblems",
abstract = "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.",
author = "L.F.P. Etman and A.A. Groenwold and J.E. Rooda",
year = "2012",
doi = "10.1007/s00158-011-0739-3",
language = "English",
volume = "45",
pages = "479--488",
journal = "Structural and Multidisciplinary Optimization",
issn = "1615-147X",
publisher = "Springer",
number = "4",

}

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

In: Structural and Multidisciplinary Optimization, Vol. 45, Nr. 4, 2012, blz. 479-488.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer 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 -