1,917 research outputs found
On affine scaling inexact dogleg methods for bound-constrained nonlinear systems
Within the framework of affine scaling trust-region methods for bound constrained problems, we discuss the use of a inexact dogleg method as a tool for simultaneously handling the trust-region and the bound constraints while seeking for an approximate minimizer of the model. Focusing on bound-constrained systems of nonlinear equations, an inexact affine scaling method for large scale problems, employing the inexact dogleg procedure, is described. Global convergence results are established without any Lipschitz assumption on the Jacobian matrix, and locally fast convergence is shown under standard assumptions. Convergence analysis is performed without specifying the scaling matrix used to handle the bounds, and a rather general class of scaling matrices is allowed in actual algorithms. Numerical results showing the performance of the method are also given
A nonmonotone trust-region method of conic model for unconstrained optimization
AbstractIn this paper, we present a nonmonotone trust-region method of conic model for unconstrained optimization. The new method combines a new trust-region subproblem of conic model proposed in [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231] with a nonmonotone technique for solving unconstrained optimization. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments are conducted to compare this method with the method of [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231]
Min Max Generalization for Two-stage Deterministic Batch Mode Reinforcement Learning: Relaxation Schemes
We study the minmax optimization problem introduced in [22] for computing
policies for batch mode reinforcement learning in a deterministic setting.
First, we show that this problem is NP-hard. In the two-stage case, we provide
two relaxation schemes. The first relaxation scheme works by dropping some
constraints in order to obtain a problem that is solvable in polynomial time.
The second relaxation scheme, based on a Lagrangian relaxation where all
constraints are dualized, leads to a conic quadratic programming problem. We
also theoretically prove and empirically illustrate that both relaxation
schemes provide better results than those given in [22]
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