Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Optimization is of vital importance when performing intensity modulated radiation therapy to treat cancer tumors. The optimization problem is typically large-scale with a nonlinear objective function and bounds on the variables, and  solve it using a quasi-Newton sequential quadratic programming method. This study investigates the effect on the optimal solution, and hence treatment outcome, when solving an approximate optimization problem of lor dimension. Through a spectral decompostion, eigenvectors and eigenvalues of an approximation to the Hessian are computed. An approximate optimization problem of reduced dimension is formulated by introducing eigenvector ights as optimization parameters, where only eigenvectors corresponding to large eigenvalues are included. The approach is evaluated on a clinical prostate case. Compared to bixel ight optimization, eigenvector ight optimization with few parameters results in faster initial decline in the objective function, but with inferior final solution. Another approach, which combines eigenvector ights and bixel ights as variables, gives lor final objective values than what bixel ight optimization does. Hover, this advantage comes at the expense of the pre-computational time for the spectral decomposition. Copyright Springer Science + Business Media, LLC 2006
['Fredrik Carlsson', 'Anders Forsgren', 'Henrik Rehbinder', 'Kjell Eriksson']
I am writing a research paper on a idea Using eigenstructure of the Hessian to reduce the dimension of the intensity modulated radiation therapy optimization problem
[{"from": "human", "value": "I am writing a research paper on a idea Using eigenstructure of the Hessian to reduce the dimension of the intensity modulated radiation therapy optimization problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Optimization is of vital importance when performing intensity modulated radiation therapy to treat cancer tumors. The optimization problem is typically large-scale with a nonlinear objective function and bounds on the variables, and  solve it using a quasi-Newton sequential quadratic programming method. This study investigates the effect on the optimal solution, and hence treatment outcome, when solving an approximate optimization problem of lor dimension. Through a spectral decompostion, eigenvectors and eigenvalues of an approximation to the Hessian are computed. An approximate optimization problem of reduced dimension is formulated by introducing eigenvector ights as optimization parameters, where only eigenvectors corresponding to large eigenvalues are included. The approach is evaluated on a clinical prostate case. Compared to bixel ight optimization, eigenvector ight optimization with few parameters results in faster initial decline in the objective function, but with inferior final solution. Another approach, which combines eigenvector ights and bixel ights as variables, gives lor final objective values than what bixel ight optimization does. Hover, this advantage comes at the expense of the pre-computational time for the spectral decomposition. Copyright Springer Science + Business Media, LLC 2006"}]