A Class of Active-Set Newton Methods for Mixed ComplementarityProblems

On a Nonsmooth Newton Methodfor Nonlinear Complementarityproblems in Function Space

Numerical Results for a Globalized Active-set Newton Method for Mixed Complementarity

We discuss a globalization scheme for a class of active-set Newton methods for solving the mixed complementarity problem (MCP), which was proposed by the authors in [3]. The attractive features of the local phase of the method are that it requires solving only one system of linear equations per iteration, yet the local superlinear convergence is guaranteed under extremely mild assumptions, in p...

On the Behavior of Damped Quasi-Newton Methods for Unconstrained Optimization

We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...

Mesh Independence and Fast Local Convergence of a Primal-dual Active-set Method for Mixed Control-state Constrained Elliptic Control Problems

A class of mixed control-state constrained optimal control problems for elliptic partial differential equations arising, for example, in Lavrentiev-type regularized state constrained optimal control is considered. Its numerical solution is obtained via a primal-dual activeset method, which is equivalent to a class of semi-smooth Newton methods. The locally superlinear convergence of the active-...

A class of multi-agent discrete hybrid non linearizable systems: Optimal controller design based on quasi-Newton algorithm for a class of sign-undefinite hessian cost functions

 In the present paper, a class of hybrid, nonlinear and non linearizable dynamic systems is considered. The noted dynamic system is generalized to a multi-agent configuration. The interaction of agents is presented based on graph theory and finally, an interaction tensor defines the multi-agent system in leader-follower consensus in order to design a desirable controller for the noted system. A...