We discuss the difficulties of estimating quadratic functionals based on observations Y (t) from the white noise model Y (t) = Jf (u )du + cr W (t), t E [0,1], o where W (t) is a standard Wiener process on [0, 1]. The optimal rates of convergence (as cr -> 0) for estimating quadratic functionals under certain geometric constraints are 1 found. Specially, the optimal rates of estimating J[f (k)(...

In this paper, the strictly convex quadratic program (QP) arising in model predictive control for constrained linear systems is reformulated as a system of piecewise affine equations. A regularized piecewise smooth Newton method with exact line-search on a convex, differentiable, piecewise-quadratic merit function is proposed for the solution of the reformulated problem. The algorithm has consi...

We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351–369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the presence o...

‎in this paper‎, ‎we propose a feasible interior-point method for‎ ‎convex quadratic programming over symmetric cones‎. ‎the proposed algorithm relaxes the‎ ‎accuracy requirements in the solution of the newton equation system‎, ‎by using an inexact newton direction‎. ‎furthermore‎, ‎we obtain an‎ ‎acceptable level of error in the inexact algorithm on convex‎ ‎quadratic symmetric cone programmin...

We propose an efficient search algorithm to solve the equation x3 + y3 + 2z3 = n for a fixed value of n > 0. By parametrizing |z|, this algorithm obtains |x| and |y| (if they exist) by solving a quadratic equation derived from divisors of 2|z|3±n. Thanks to the use of several efficient numbertheoretic sieves, the new algorithm is much faster on average than previous straightforward algorithms. ...

today, with rapid growth of the world wide web and creation of internet sites and online text resources, text summarization issue is highly attended by various researchers. extractive-based text summarization is an important summarization method which is included of selecting the top representative sentences from the input document. when, we are facing into large data volume documents, the extr...

in this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. some examples are provided to show the accuracy and reliability of the proposed method. it is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to t...