TY - GEN

T1 - A sequential quadratic programming with an approximate Hessian matrix update using an enhanced two-point diagonal quadratic approximation

AU - Jung, Sangjin

AU - Choi, Dong Hoon

AU - Choi, Gyunghyun

N1 - Funding Information:
This research was supported by the Multi-Material Mix (MMM) Ultra-Light Body Development Program, the Automobile Component Base Technology Development Program, the International Cooperation of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) (No. 20102030200011) and the c-MES platform for Productivity Innovation & Process Optimizing of SME Program in the Ministry of Knowledge Economy.

PY - 2010

Y1 - 2010

N2 - A Broyden-Fletcher-Goldfarb-Shanno (BFGS) update formula is a standard technique for updating the Hessian matrix of a Lagrangian function in a sequential quadratic programming (SQP). The initial Hessian of the SQP is usually set to an identity matrix, because the previous information of the Hessian does not exist at the first iteration and it is extremely expensive to evaluate the exact Hessian of the real Lagrangian function. The inaccuracy of the identity matrix, however, is propagated to the next iterations in the SQP using BFGS update formula. In this study, we develop a new method that can generate more accurate approximate Hessian than that using the BFGS update formula even if the identity matrix is employed at the first iteration. In this method, the inaccuracy of the identity matrix is not propagated to the next iterations. Since the approximate Lagrangian obtained by using an enhanced two-point diagonal quadratic approximation method can be expressed as an explicit function of the design variables, the Hessian of the approximate Lagrangian can be analytically evaluated with negligible computational cost.

AB - A Broyden-Fletcher-Goldfarb-Shanno (BFGS) update formula is a standard technique for updating the Hessian matrix of a Lagrangian function in a sequential quadratic programming (SQP). The initial Hessian of the SQP is usually set to an identity matrix, because the previous information of the Hessian does not exist at the first iteration and it is extremely expensive to evaluate the exact Hessian of the real Lagrangian function. The inaccuracy of the identity matrix, however, is propagated to the next iterations in the SQP using BFGS update formula. In this study, we develop a new method that can generate more accurate approximate Hessian than that using the BFGS update formula even if the identity matrix is employed at the first iteration. In this method, the inaccuracy of the identity matrix is not propagated to the next iterations. Since the approximate Lagrangian obtained by using an enhanced two-point diagonal quadratic approximation method can be expressed as an explicit function of the design variables, the Hessian of the approximate Lagrangian can be analytically evaluated with negligible computational cost.

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U2 - 10.2514/6.2010-9130

DO - 10.2514/6.2010-9130

M3 - Conference contribution

AN - SCOPUS:84880785772

SN - 9781600869549

T3 - 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 2010

BT - 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 2010

T2 - 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, MAO 2010

Y2 - 13 September 2010 through 15 September 2010

ER -