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Conjugate gradient methods are well known and popular in unconstrained optimization. Numerous studies and modifications have been devoted by researchers to improve this method. In this paper, we introduced a new conjugate gradient coefficient (βk) and tested its performance using exact line search. Numerical results based on number of iterations have shown our new βk performance is better or equivalent...
The Perry conjugate gradient method is generalized, from which a new descent algorithm, PDCGy, is presented and its global convergence is proven under Wolfe line searches. Preliminary numerical results for a set of 720 unconstrained optimization test problems verify the performance of the algorithm and show that the PDCGy algorithm is competitive with the CG_DESCENT algorithm.
In this paper, we propose a new super-memory gradient method for unconstrained optimization problems. The global convergence and linear convergence rate are proved under some mild conditions. The method uses the current and previous iterative information to generate a new search direction and uses Wolfe line search to define the step-size at each iteration. It has a possibly simple structure and avoids...
Conjugate gradient methods are widely used for large scale unconstrained optimization. A new class of conjugate gradient trust region method is proposed, in which trust region technique is used for guaranteeing the global convergence of the algorithm, and more utilizable information on conjugate gradient vectors is used for accelerating convergence of the algorithm. The global convergence, super linear...
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.
Conjugate gradient methods are important for large-scale unconstrained optimization. In this paper, we propose anew formula ??k for unconstrained optimization, which is the hybrid from HS method, LS method and CD method. From the construction of the new formula ??k, we use a direction which is different from traditional dk. The direction satisfies descent conditions naturally. And dkTgk=-??gk??2...
In this paper, we present several dynamical systems for efficient and accurate computation of optimal low rank approximation of a real matrix. The proposed dynamical systems are gradient flows or weighted gradient flows derived from unconstrained optimization of certain objective functions. These systems are then modified to obtain power-like methods for computing a few dominant singular triplets...
An un-unconstrained optimization problem involving logarithmic cost function that incorporates a diagonal matrix is utilized for deriving gradient dynamical systems that converge to the principal singular components of arbitrary matrix. The equilibrium points of the resulting gradient systems are determined and their stability is thoroughly analyzed. Qualitative properties of the proposed systems...
This paper considers the problem of optical signal-to-noise ratio (OSNR) optimization with link capacity constraints within a Nash game framework. In optical wavelength-division multiplexed (WDM) networks, all wavelength-multiplexed channels share the optical fiber. Even when individually channel parameters are adjusted, the total launched power has to be limited below the nonlinearity threshold....
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