A relaxation method for nonconvex quadratically constrained quadratic programs

Al-Khayyal, Faiz A.; Larsen, Christian; Voorhis, Tim Van

doi:10.1007/bf01099462

Cited by 91 publications

(28 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is done by solving the optimization 3 up to second order-a standard linear constraint quadratic programming problem. Numerical techniques 17 exist that can nd global maximums of a z i z Sz subject to \ z \ . Current software…”

Section: Synthesismentioning

confidence: 99%

See 1 more Smart Citation

Symmetry Approach to Extension of Flutter Boundaries via Mistuning

Shapiro

1998

Journal of Propulsion and Power

View full text Add to dashboard Cite

A general framework is presented for analyzing and optimizing stability increases resulting from mistuning. The framework given is model independent and is based primarily on symmetry arguments. Dif cult practical issues are transformed to tractable mathematical questions. It is shown that mistuning analysis reduces to a block circular matrix eigenvalue /vector problem that can be solved ef ciently even for large problems. Similarly, the optimization becomes a standard linear constraint quadratic programming problem and can be solved numerically. Because the methods given are model-independent, they can be applied to various models and allow the researcher to easily conclude which models accurately capture mistuning and which do not. A simple quasisteady model for utter in a cascade is used to illustrate and validate results in this paper.Nomenclature a = linear stability coef cient, Eqs. (13), (14), and (35) b = diagonal quadratic stability coef cient, Eqs. (13), (14), and (36) c i = ith off-diagonal quadratic stability coef cient, Eqs.

show abstract

Section: Synthesismentioning

confidence: 99%

“…Consequently, the optimization becomes a linear constaint quadratic program. Using branch and bound software developed by Faiz et al 17 it is possible to nd global optimums for fairly large problems (up to about 30 blades). More realistic constraints motivated by side effects in general and mode localization in particular shall be addressed in future research.…”

mentioning

confidence: 99%

Symmetry Approach to Extension of Flutter Boundaries via Mistuning

Shapiro

1998

Journal of Propulsion and Power

View full text Add to dashboard Cite

show abstract

“…We can nd global optima for this problem by using a branch and bound method. 11 In both cases A and B, the optimal solution is in the ' rst' mode z ¤ D .²; ²; : : : ; ²; ¡²; ¡²; : : : ; ¡²/. The advantageof our optimization problem phrased above is that it is globally tractable and it improves both utter boundaries and forced response.…”

Section: Intentional Robust Optimal Mistuningmentioning

confidence: 99%

Analyzing Mistuning of Bladed Disks by Symmetry and Reduced-Order Aerodynamic Modeling

Shapiro

Willcox

2003

Journal of Propulsion and Power

View full text Add to dashboard Cite

“…Tseng [8] further studied approximation bounds of the SDP relaxation for the NQP. When constraint functions include nonconvex quadratic constraint, based on outer approximation method and linear programming relaxation a branch-and-bound method for solving the NQP was proposed in [9]; based on linear programming relaxation technique, two simplicial branch-and-bound algorithms were presented for solving the NQP in Refs. [10,11], respectively.…”

Section: Introductionmentioning

confidence: 99%