We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate and variable sample size strategy employed. proposed algorithm combines an SAA subgradient spectral coefficient order provide suitable direction which improves performance first method as shown by numerical results....

The purpose of this article is to introduce a general inertial projected gradient method with self-adaptive stepsize for solving variational inequality problems. proposed incorporates two different extrapolations respect the previous iterates into method. weak convergence our proved under standard assumptions without any requirement knowledge Lipschitz constant mapping. Furthermore, R-linear ra...

Based on the augmented Lagrangian strategy, we propose a projected gradient method for solving the high-order model in image restoration problems. Based on the Bermùdez and Moreno (BM) algorithm, the convergence of the proposed method is proved. We also give the relationship that the semi-implicit gradient descent method can be deduced from the projected gradient method. Some numerical experime...

An n×n correlation matrix has k factor structure if its off-diagonal agrees with that of a rank k matrix. Such correlation matrices arise, for example, in factor models of collateralized debt obligations (CDOs) and multivariate time series. We analyze the properties of these matrices and, in particular, obtain an explicit formula for the rank in the one factor case. Our main focus is on the nea...

We propose a general and efficient algorithm for learning low-rank matrices. The proposed algorithm converges super-linearly and can keep the matrix to be learned in a compact factorized representation without the need of specifying the rank beforehand. Moreover, we show that the framework can be easily generalized to the problem of learning multiple matrices and general spectral regularization...

The application of the fast gradient method to the dual QP leads to the Dual Fast Projected Gradient (DFPG) method. The DFPG converges with O ( k−2 ) rate, where k > 0 is the number of steps. At each step, it requires O(nm) operations. Therefore for a given ε > 0 an ε-approximation to the optimal dual function value

We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected N...