The generalized Nash equilibrium problem is a Nash game which, in contrast to the standard Nash equilibrium problem, allows the strategy sets of each player to depend on the decision variables of all other players. It was recently shown by the authors that this generalized Nash equilibrium problem can be reformulated as both an unconstrained and a constrained optimization problem with continuou...

Control forces in semi-active control systems are constrained by the dynamics of actuators that regulate energy transmission through variable damping and/or stiffness mechanisms. The potential benefit of the development and implementation of new semi-active control devices and applications can be determined by optimizing the controlled performance subject to the constraints of the dynamics of t...

A new filter-trust-region algorithm for solving unconstrained nonlinear optimization problems is introduced. Based on the filter technique introduced by Fletcher and Leyffer, it extends an existing technique of Gould, Leyffer, and Toint [SIAM J. Optim., 15 (2004), pp. 17–38] for nonlinear equations and nonlinear least-squares to the fully general unconstrained optimization problem. The new algo...

This paper proposes a novel approach to L2sensitivity minimization problem of state-space digital filters subject to L2-scaling constraints. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. As a result, iterative algorithms for the L2-sensitivity minimization without L2-scaling constraints can be ...

Abstract For the unconstrained optimization of black box functions, this paper introduces a new randomized algorithm called . In practice, matches quality other state-of-the-art algorithms for finding, in small and large dimensions, local minimizer with reasonable accuracy. Although our theory guarantees only minimizers heuristic techniques turn into an efficient global solver. very thorough nu...

Our interest lies in solving large-scale unconstrained SOS (sum of squares) polynomial optimization problems. Because interior-point methods for solving these problems are severely limited by the large-scale, we are motivated to explore efficient implementations of an accelerated first-order method to solve this class of problems. By exploiting special structural properties of this problem clas...

A numerical method for solving the H∞ synthesis problem is presented. The problem is posed as an unconstrained, nonsmooth, nonconvex minimization problem. The optimization variables consist solely of the entries of the output feedback matrix. No additional variables, such as Lyapunov variables, need to be introduced. The optimization procedure uses a line search mechanism where the descent dire...

A numerical method for solving the H∞ synthesis problem is presented. The problem is posed as an unconstrained, nonsmooth, nonconvex minimization problem. The optimization variables consist solely of the entries of the output feedback matrix. No additional variables, such as Lyapunov variables, need to be introduced. The optimization procedure uses a line search mechanism where the descent dire...

A well-known technique for the solution of quasi-variational inequalities (QVIs) consists in the reformulation of QVIs as a constrained or unconstrained optimization problem by means of so-called gap functions. In contrast to standard variational inequalities, however, these gap functions turn out to be nonsmooth in general. Here it is shown that one can obtain an unconstrained optimization ref...