Nataša Krejić In many cases in which one wishes to minimize a complicated or expensive function, it is convenient to employ cheap approximations, at least when the current approximation to the solution is poor. Adequate strategies for deciding the accuracy desired at each stage of optimization are crucial for the global convergence and overall efficiency of the … Read more
Convex and nonconvex finite-sum minimization arises in many scientific computing and machine learning applications. Recently, first-order and second-order methods where objective functions, gradients and Hessians are approximated by randomly sampling components of the sum have received great attention. We propose a new trust-region method which employs suitable approximations of the objective function, gradient and Hessian … Read more
This paper deals with the minimization of large sum of convex functions by Inexact Newton (IN) methods employing subsampled Hessian approximations. The Conjugate Gradient method is used to compute the inexact Newton step and global convergence is enforced by a nonmonotone line search procedure. The aim is to obtain methods with affordable costs and fast … Read more
We consider unconstrained minimization of a finite sum of $N$ continuously differentiable, not necessarily convex, cost functions. Several gradient-like (and more generally, line search) methods, where the full gradient (the sum of $N$ component costs’ gradients) at each iteration~$k$ is replaced with an inexpensive approximation based on a sub-sample~$\mathcal N_k$ of the component costs’ gradients, … Read more
We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are attractive due to their inexpensive iterations, but have a drawback of slow convergence rates. This motivates the incorporation of second-order information … Read more
We consider the Spectral Projected Gradient method for solving constrained optimization problems with the objective function in the form of mathematical expectation. It is assumed that the feasible set is convex, closed and easy to project on. The objective function is approximated by a sequence of Sample Average Approximation functions with different sample sizes. The … Read more
We consider distributed optimization where $N$ nodes in a connected network minimize the sum of their local costs subject to a common constraint set. We propose a distributed projected gradient method where each node, at each iteration $k$, performs an update (is active) with probability $p_k$, and stays idle (is inactive) with probability $1-p_k$. Whenever … Read more
Nonmonotone line search methods for unconstrained minimization with the objective functions in the form of mathematical expectation are considered. The objective function is approximated by the sample average approximation (SAA) with a large sample of fixed size. The nonmonotone line search framework is embedded with a variable sample size strategy such that different sample size … Read more
Minimization of unconstrained objective function in the form of mathematical expectation is considered. Sample Average Approximation – SAA method transforms the expectation objective function into a real-valued deterministic function using large sample and thus deals with deterministic function minimization. The main drawback of this approach is its cost. A large sample of the random variable … Read more