Constrained and unconstrained optimization pdf

Posted on Monday, March 15, 2021 7:40:11 AM Posted by Fletcher P. - 15.03.2021 and pdf, pdf free download 0 Comments

constrained and unconstrained optimization pdf

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Show all documents Under the suitable conditions, the global convergence with the SWP line search rule and the weak Wolfe-Powell WWP line search rule is established for nonconvex function. Copyright q Gonglin Yuan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Then, based on this modified secant relation we present a new BFGS method for solving unconstrained optimization problems.

Algorithms for Constrained and Unconstrained Optimization Calculations

An unconstrained minimizer of a general nonlinear function may be found by solving a sequence of constrained subproblems in which a quadratic model function is minimized subject to a "trust-region" constraint on the norm of the change in variables. For the large-scale case, Steihaug has proposed an iterative method for the constrained subproblem based on the preconditioned conjugate-gradient PCG method.

This method is terminated inside the trust region at an approximate minimizer or at the point where the iterates cross the trust-region boundary. When the iterates are terminated at the trust- region boundary, the final iterate is generally an inaccurate solution of the constrained subproblem.

This may have an adverse affect on the efficiency and robustness of the overall trust-region method. A PCG-based method is proposed that may be used to solve the trust- region subproblem to any prescribed accuracy.

The method starts by using a modified Steihaug method. If the solution lies on the trust-region boundary, a PCG-based sequential subspace minimization SSM method is used to solve the constrained problem over a sequence of evolving low-dimensional subspaces. A new regularized sequential Newton method is used to define basis vectors for the subspace minimization.

Several preconditioners are proposed for the PCG iterations. Numerical results suggest that, in general, a trust-region method based on the proposed solver is more robust and requires fewer function evaluations than Steihaug's method. Skip to main content. UC San Diego. Email Facebook Twitter. Abstract An unconstrained minimizer of a general nonlinear function may be found by solving a sequence of constrained subproblems in which a quadratic model function is minimized subject to a "trust-region" constraint on the norm of the change in variables.

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UC San Diego

A brief survey is given of the main ideas that are used in current optimization algorithms. Attention is given to the purpose of each technique instead of to its details. It is believed that all the techniques that are mentioned are important to the development of useful algorithms. Unable to display preview. Download preview PDF. Skip to main content.

UC San Diego

Ricardo A. Silveira, Wellington L. Pereira, Paulo B.

An unconstrained minimizer of a general nonlinear function may be found by solving a sequence of constrained subproblems in which a quadratic model function is minimized subject to a "trust-region" constraint on the norm of the change in variables. For the large-scale case, Steihaug has proposed an iterative method for the constrained subproblem based on the preconditioned conjugate-gradient PCG method. This method is terminated inside the trust region at an approximate minimizer or at the point where the iterates cross the trust-region boundary. When the iterates are terminated at the trust- region boundary, the final iterate is generally an inaccurate solution of the constrained subproblem.

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