We describe a block matrix iterative algorithm for solving a linearquadratic parabolic optimal control problem (OCP) on a finite time interval. We derive a reduced symmetric indefinite linear system involving the control variables and auxiliary variables, and solve it using a preconditioned MINRES iteration, with a symmetric positive definite block diagonal preconditioner based on the parareal ...

This paper addresses robust H∞ control problems for nonlinear systems with parameter uncertainty. By using the technique of partition of unity, necessary and sufficient conditions for existence of strong robust H∞ dynamic compensators and static state feedback controllers are established in terms of nonlinear matrix inequality (NLMI) approach, respectively. These conditions reduce the robust H∞...

One of the factors that add to the complexity of the cutting stock problem is the large number of the cutting patterns that may be encountered. When the cutting stock problem is expressed as an integer-programming problem, the large number of cutting patterns involved generally makes computation infeasible. However, if the linear programming formulation of the cutting stock problem is free of i...

Factorization machines offer an advantage over other existing collaborative filtering approaches to recommendation. They make it possible to work with any auxiliary information that can be encoded as a real-valued feature vector as a supplement to the information in the user-item matrix. We build on the assumption that different patterns characterize the way that users interact with (i.e., rate...

To improve the efficiency of medical staff in surgical operations and meet physiological psychological needs surgeons, nurses, patients during operations, auxiliary equipment is designed. This paper builds a design research model based on AHP (analytic hierarchy process), QFD (quality function deployment), Platts conceptual decision matrix (PUGH matrix). Firstly, user requirements are weighed t...

This paper proposes sufficient conditions to the regional stability analysis of switched nonlinear systems with time-varying parameters. The nonlinear sub-modes of operation are described by means of differential-algebraic equations involving the state and an auxiliary nonlinear vector. We then use piecewise polynomial Lyapunov functions and a relaxation technique that lead to a convex characte...

The nonlocality in the path integral description of the reduced density matrix for a system interacting with a classical harmonic bath can be eliminated through the introduction of auxiliary variables, leading to Markovian equations. By contrast, the presence of an imaginary part in quantum mechanical response functions appears to prohibit similar approaches, necessitating explicit treatment of...

A new Neumann-Neumann type domain decomposition algorithm for the solution of contact problems of elasticity and similar problems is described. The discretized variational inequality that models the equilibrium of a system of elastic bodies in contact is first turned by duality to a strictly convex quadratic programming problem with either box constraints or box and equality constraints. This s...

A right-preconditioning process for linear interval systems has been presented by Neumaier in 1987. It allows the construction of an outer estimate of the united solution set of a square linear interval system in the form of a parallelepiped. The denomination ”right-preconditioning” is used to describe the preconditioning processes which involve the matrix product AC in contrast to the (usual) ...