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To address the unconstrained optimization problem, the Conjugate Gradient Method (CG) uses the sequence of iterations to approach the minimum point of aim function. Because of the effect of rounding errors, many merits of CG are no longer in existence in practical use. Hence the rate of convergence is not ideal and a practical problem confronting us is how to improve conjugate gradient iteration so...
We propose a new trust region method that employs both the modified BFGS update and Amijio line search. The method exploits the information of function and gradient, and ensures the Hessian matrix of trust region subproblem positive-definite. At some assumptions, the global convergence and superlinear convergence property are proposed. Finally, numerical experiments show that the method is efficient.
In practice, the convergence rate and stability of perturbation based extremum-seeking (ES) schemes can be very sensitive to the curvature of the plant map. This sensitivity arises from the use of a gradient descent adaptation algorithm. Such ES schemes may need to be conservatively tuned in order to maintain stability over a wide range of operating conditions, resulting in slower optimisation than...
In this paper we develop a new dual decomposition method for optimizing a sum of convex objective functions corresponding to multiple agents but with coupled constraints. In our method we define a smooth Lagrangian, by using a smoothing technique developed by Nesterov, which preserves separability of the problem. With this approach we propose a new decomposition method (the proximal center method)...
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