Determining the search direction and the search step are the two main steps of the nonlinear optimization algorithm,in which the derivatives of the objective and constraint functions are used to determine the search d...Determining the search direction and the search step are the two main steps of the nonlinear optimization algorithm,in which the derivatives of the objective and constraint functions are used to determine the search direction,the one-dimensional search and the trust domain methods are used to determine the step length along the search direction.One dimensional line search has been widely discussed in various textbooks and references.However,there is a lessknown techniquearc-search method,which is relatively new and may generate more efficient algorithms in some cases.In this paper,we will survey this technique,discuss its applications in different optimization problems,and explain its potential improvements over traditional line search method.展开更多
In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the ent...In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the entire central path. The favorable polynomial complexity bound of the algorithm is obtained, namely O（nlog（（ x^0）~TS^0/ε）） which is as good as the linear programming analogue. Finally, the numerical experiments show that the proposed algorithm is efficient.展开更多
文摘Determining the search direction and the search step are the two main steps of the nonlinear optimization algorithm,in which the derivatives of the objective and constraint functions are used to determine the search direction,the one-dimensional search and the trust domain methods are used to determine the step length along the search direction.One dimensional line search has been widely discussed in various textbooks and references.However,there is a lessknown techniquearc-search method,which is relatively new and may generate more efficient algorithms in some cases.In this paper,we will survey this technique,discuss its applications in different optimization problems,and explain its potential improvements over traditional line search method.
基金Supported by the National Natural Science Foundation of China(71471102)
文摘In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the entire central path. The favorable polynomial complexity bound of the algorithm is obtained, namely O（nlog（（ x^0）~TS^0/ε）） which is as good as the linear programming analogue. Finally, the numerical experiments show that the proposed algorithm is efficient.
