This study concerns with a trust-region-based method for solving unconstrained optimization problems. The approach takes the advantages of the compact limited memory BFGS updating formula together with an appropriate adaptive radius strategy. In our approach, the adaptive technique leads us to decrease the number of subproblems solving, while utilizing the structure of limited memory quasi-Newt...

We introduce an unconstrained multicriteria optimization problem and discuss its relation to various well-known scalar robust optimization problems with a finite uncertainty set. Specifically, we show that a unique solution of a robust optimization problem is Pareto optimal for the unconstrained optimization problem. Furthermore, it is demonstrated that the set of weakly Pareto optimal solution...

In the first part of the tutorial, we introduced the problem of unconstrained optimization, provided necessary and sufficient conditions for optimality of a solution to this problem, and described the gradient descent method for finding a (locally) optimal solution to a given unconstrained optimization problem. We now describe another method for unconstrained optimization, namely Newton’s metho...

In this paper we give an review on convergence problems of un-constrained optimization algorithms, including line search algorithms and trust region algorithms. Recent results on convergence of conjugate gradient methods are discussed. Some well-known convergence problems of variable metric methods and recent eeorts made on these problems are also presented.

A local minimum is a point at which the value of the function is less than or equal to all immediately nearby or surrounding function values. A global minimum realizes the smallest possible value of the function over all feasible inputs. In general, based purely on local knowledge of a function and its behavior, it can be very difficult to distinguish whether you have discovered a local or a gl...