A new approach to minimax MPC for systems with bounded external system disturbances and measurement errors is introduced. It is shown that joint deterministic state estimation and minimax MPC can be written as an optimization problem with linear and quadratic matrix inequalities. By linearizing the quadratic matrix inequality, a semidefinite program is obtained. A simulation study indicates tha...

In 1929, the KKMmap was introduced by Knaster et al. [13] and it provides the foundation for many well-known existence results, such as Ky Fan’s minimax inequality theorem, Ky Fan-Browder’s fixed point theorem, Nash’s equilibrium theorem, HartmanStampacchia’s variational inequality theorem and many others (see [1, 2, 5–12, 14–17]). The central idea of applying KKM theory to prove that a family ...

As argued in the proof sketch of Theorem 2, it suffices to show that r ,ε,k,n (Q) obeys the data processing inequality. is the minimax risk in the non-private setting.

Fan’s minimax inequality is extended to the context of metric spaces with global nonpositive curvature. As a consequence, a much more general result on the existence of a Nash equilibrium is obtained. © 2009 Elsevier Ltd. All rights reserved.

This paper presents a neural network for solving non-linear minimax multiobjective fractional programming problem subject to nonlinear inequality constraints. Neural model is designed for optimization with constraints condition. Methodology is based on the lagrange multiplier with saddle point optimization.

The aim of this paper is to show a simple way to construct asymptotic minimax lower bounds for risks based on different types of quadratic loss functions in semiparametric inference problems. For the sake of clarity, we consider the simple case of the state estimation of a dynamical system with small noise. The proofs are based on the van Trees inequality, namely an integral type Cramér-Rao ine...

The aim of this article is to show a simple way to construct asymptotic minimax lower bounds for risks based on different types of quadratic loss functions in semiparametric inference problems. For the sake of clarity, we consider the simple case of the state estimation of a dynamical system with small noise. The proofs are based on the van Trees inequality, namely, an integral-type Cramér-Rao ...