An Inexact Regularized Newton Framework with a Worst-Case Iteration Complexity of $\mathcal{O}(\epsilon^{-3/2})$ for Nonconvex Optimization

An algorithm for solving smooth nonconvex optimization problems is proposed that, in the worst-case, takes $\mathcal{O}(\epsilon^{-3/2})$ iterations to drive the norm of the gradient of the objective function below a prescribed positive real number $\epsilon$ and can take $\mathcal{O}(\epsilon^{-3})$ iterations to drive the leftmost eigenvalue of the Hessian of the objective above $-\epsilon$. The proposed … Read more

Globally Convergent Primal-Dual Active-Set Methods with Inexact Subproblem Solves

We propose primal-dual active-set (PDAS) methods for solving large-scale instances of an important class of convex quadratic optimization problems (QPs). The iterates of the algorithms are partitions of the index set of variables, where corresponding to each partition there exist unique primal-dual variables that can be obtained by solving a (reduced) linear system. Algorithms of … Read more

An Inexact Sequential Quadratic Optimization Algorithm for Nonlinear Optimization

We propose a sequential quadratic optimization method for solving nonlinear optimization problems with equality and inequality constraints. The novel feature of the algorithm is that, during each iteration, the primal-dual search direction is allowed to be an inexact solution of a given quadratic optimization subproblem. We present a set of generic, loose conditions that the … Read more

On affine scaling inexact dogleg methods for bound-constrained nonlinear systems

A class of trust-region methods for large scale bound-constrained systems of nonlinear equations is presented. The methods in this class follow the so called affine-scaling approach and can efficiently handle large scale problems. At each iteration, a suitably scaled region around the current approximate solution is defined and, within such a region, the norm of … Read more

An interior Newton-like method for nonnegative least-squares problems with degenerate solution

An interior point approach for medium and large nonnegative linear least-squares problems is proposed. Global and locally quadratic convergence is shown even if a degenerate solution is approached. Viable approaches for implementation are discussed and numerical results are provided. Citation Technical Report 1/2005, Dipartimento di Energetica ‘S. Stecco’, Universita di Firenze, Italia Article Download View … Read more