A. S. Bandeira In this paper we consider the use of probabilistic or random models within a classical trust-region framework for optimization of deterministic smooth general nonlinear functions. Our method and setting differs from many stochastic optimization approaches in two principal ways. Firstly, we assume that the value of the function itself can be computed without noise, in … Read more
Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from less points than there are basis components. Often, in practical applications, the contribution of the problem variables to the objective function is such that many pairwise correlations … Read more
In this paper we consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the l1-norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to the classical problem in Compressed Sensing where the l1-norm of the … Read more
Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from less points than there are basis components. Often, in practical applications, the contribution of the problem variables to the objective function is such that many pairwise correlations … Read more
In this paper we consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the l1-norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to the classical problem in Compressed Sensing where the l1-norm of the … Read more