As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten- p quasi-norm minimization (0 < p < 1), has been developed to approximate the rank function closely. We study the performance of projected gradient descent algorithm for solving the Schatten- ...
If the initial point and the error level \epsilon_g satisfy \|x_0-x^*\|_2^2 \leq \rho^2 and \epsilon_g^2 < \frac{c_0 \rho^2}{1.5} , then for each step t \geq 0 of the projected gradient descent algorithm with step size \eta = \frac{1}{\beta} , we have \|x_...
We develop the notion of local concavity coefficients of the constraint set, measuring the extent to which convexity is violated, which govern the behavior of projected gradient descent over this set. We demonstrate the versatility of these concavity coefficients by computing them for a range of ...
Projected Barzilai-Borwein Method with Infeasible Iterates for Nonnegative Least-Squares Image Deblurring We present a non-monotonic gradient descent algorithm with infeasible iterates for the nonnegatively constrained least-squares deblurring of images. The skewness of the intensity values of the deblurre...
On the convergence properties of the projected gradient method for convex optimization When applied to an unconstrained minimization problem with a convex objective, the steepest descent method has stronger convergence properties than in the ... AN Iusem - Comput Appl Math 被引量: 98发表: 2003年 ...
On The Convergence of Block Coordinate Descent Type Methods On the convergence of the projected gradient method for vector… On the Translation of Idioms From a Perspective of Culture on the convergence of supercritical general (c-m-j) branching processes 国际能源经济手册International Handbook on the...
For example, when the global objective function is the least squares (5), using alternating projected gradient descent is guaranteed to converge to stationary points, because the subproblems are convex and Lipschitz smooth [128]. 6.1.1 Convergence of first-order methods The effect of the number ...
Yang, W.H., Han, D.R.: Linear convergence of the alternating direction method of multipliers for a class of convex optimization problems. SIAM J. Numer. Anal. 54(2), 625–640 (2016) MathSciNet MATH Google Scholar Zhang, C., Chen, X.: Smoothing projected gradient method and its app...
of convergence of MPRGP in terms of the spectral condition number of the Hessian matrix and the proof of the finite termination property for the problems whose solution does not satisfy the strict complementarity condition. The bound on the R-linear rate of convergence of the projected gradient ...
Dai, Y.-H., Fletcher, R.: On the asymptotic behaviour of some new gradient methods. Math. Program. 103, 541–559 (2005) Article MathSciNet Google Scholar Dai, Y.-H., Fletcher, R.: Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming. Numer. Math. ...