In 1940, Ulam proposed the stability problem see 1 . Let G1 be a group, and let G2 be a metric group with the metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a mapping h : G1 → G2 satisfies the inequality d h xy , h x h y < δ for all x, y ∈ G1 then there is a homomorphism H : G1 → G2 with d h x ,H x < ε for all x ∈ G1? In 1941, this problem was solved by Hyers 2 in the case o...

The present study aimed to investigate the changes of Rho-associated kinase (Rho-kinase) and neuronal nitric oxide synthase (nNOS) expression in age-associated erectile dysfunction (ED) in Sprague-Dawley (SD) rats. A total of 100 intact male SD rats were divided into 20 groups according to their age (5-24 months; rats that were the same age in months were in the same group). Erectile response m...

We consider a generalized proximal point method for solving variational inequalities with maximal monotone operators in a Hilbert space. It proves to be that the conditions on the choice of a non-quadratic distance functional depend on the geometrical properties of the operator in the variational inequality, and – in particular – a standard assumption on the strict convexity of the kernel of th...

An analytical solution is provided to the problem of minimising a convex quadratic under a general quadratic (inequality) constraint, additional affine constraints being easily accommodated. Such problems occur widely. The explicit, analytical solution provided offers insight into the diverse nature both of special cases of this problem and of their solution sets. This sheds light on algorithm ...

In this paper, we propose a method to design robust sliding hyperplanes in the presence of mismatched parametric uncertainty based on quadratic stability. The robust sliding hyperplane is constructed from a Riccati inequality associated with quadratic stabilizability. The proposed method enables us to deal with structured uncertainty and optimize the sliding motion by applying the guaranteed co...

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...

Two seemingly independent streams of control systems research have examined logarithmic sensitivity integrals and limiting linear quadratic optimal control problems. These apparently diverse problems yield some results with an identical right hand side. The main contribution of this paper is to directly explain the commonality between these streams. This explanation involves the use of Parseval...

PERMON makes use of theoretical results in quadratic programming algorithms and domain decomposition methods. It is built on top of the PETSc framework for numerical computations. This paper describes its fundamental packages and shows their applications. We focus here on contact problems of mechanics decomposed by means of a FETI-type nonoverlapping domain decomposition method. These problems ...

In this work we propose an outcome space approach for globally solving generalized concave multiplicative problems, a special class of nonconvex problems which involves the maximization of a finite sum of products of concave functions over a nonempty compact convex set. It is shown that this nonconvex maximization problem can be reformulated as an indefinite quadratic problem with infinitely ma...

Recently, Wright proposed a stabilized sequential quadratic programming algorithm for inequality constrained optimization. Assuming the Mangasarian-Fromovitz constraint qualification and the existence of a strictly positive multiplier (but possibly dependent constraint gradients), he proved a local quadratic convergence result. In this paper, we establish quadratic convergence in cases where bo...