A trust region method for zero-one nonlinear programming (original) (raw)
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In this paper, we present a new trust region method for unconstrained nonlinear programming in which we blend adaptive trust region algorithm by non-monotone strategy to propose a new non-monotone trust region algorithm with automatically adjusted radius. Both non-monotone strategy and adaptive technique can help us introduce a new algorithm that reduces the number of iterations and function evaluations. The new algorithm preserves the global convergence and has local superlinear and quadratic convergence under suitable conditions. Numerical experiments exhibit that the new trust region algorithm is very efficient and robust for unconstrained optimization problems.
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RAL-TR-2004-009 A filter-trust-region method for unconstrained optimization
A new filter-trust-region algorithm for solving unconstrained nonlinear optimization problems is introduced. Based on the filter technique introduced by Fletcher and Leyffer, it extends an existing technique of Gould, Leyffer and Toint (SIAM J. Optim., to appear, 2004) for nonlinear equations and nonlinear least-squares to the fully general unconstrained optimization problem. The new algorithm is shown to be globally convergent to at least one second-order critical point, and numerical experiments indicate that it is very competitive with more classical trust-region algorithms. 1 Computational Science and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England, UK. Email: n.gould@rl.ac.uk 2 Current reports available from “http://www.numerical.rl.ac.uk/reports/reports.shtml”. 3 This work was supported by the EPSRC grant GR/S42170 4 Department of Mathematics, Facultés Universitaires ND de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium, EU....
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In this paper, we consider a nonlinear semi-definite programming problem that represents the fixed order H 2 and H 2 =H 1 synthesis problems. A proximal-point sequential quadratic programming method that makes use of trust region is developed. Furthermore, the constrained trust region method [F. Leibfritz, E.M.E. Mostafa, Trust region methods for solving the optimal output feedback design problem, Int. J. Contr. 76 (2003) 501-519], which was designed to solve a nonlinear semi-definite program representing the H 2 synthesis problem, is extended to solve a more general nonlinear semi-definite program representing the fixed order H 2 =H 1 synthesis problem. Numerical results for the proposed methods are given. .sa (A. Hamdi), tahoun44@yahoo.com (A. Aboutahoun). 810-832 www.elsevier.com/locate/amc Keywords: Semi-definite programming; Linear quadratic control; Nonlinear programming; Trust region methods
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In this paper, we propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This algorithm incorporates two novelties: it benefits from a radius dependent shrinkage parameter for adjusting the trust region radius that avoids undesirable directions and it exploits a new strategy to prevent sudden increments of objective function values in nonmonotone trust region techniques. Global convergence of this algorithm is investigated under some mild conditions. Numerical experiments demonstrate the efficiency and robustness of the proposed algorithm in solving a collection of unconstrained optimization problems from the CUTEst package.
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