In this paper we consider optimization problems de ned by a quadratic objective function and a nite number of quadratic inequality constraints. Given that the objective function is bounded over the feasible set, we present a comprehensive study of the conditions under which the optimal solution set is nonempty, thus extending the so-called Frank-Wolfe theorem. In particular, we rst prove a gene...

This paper deals with the problem of delay-dependent stability criterion of uncertain periodic switched recurrent neural networks with time-varying delays.When uncertain discrete-time recurrent neural network is a periodic system, it is expressed as switched neural network for the finite switching state. Based on the switched quadratic Lyapunov functional approach SQLF and freeweighting matrix ...

This paper presents an approach to compute the neighboring extremal solution for an optimal switched impulsive control problem with a pre-specified sequence of modes and a large perturbation in the initial state. The decision variables – the subsystem switching times and the control parameters – are subject to inequality constraints. Since the active status of these inequality constraints may c...

Abstract: Quadratic programming problems are widespread class of nonlinear programming problems with many practical applications. The case of inequality constraints have been considered in a previous author’s paper. Later on an extension of these results for the case of inequality and equality constraints has been proposed. Based on equivalent formulation of Kuhn-Tucker conditions, a new neural...

We revisit the classical Poincaré inequality on closed surfaces, and prove its natural analogue for quadratic differentials. In stark contrast to the classical case, our inequality does not degenerate when we work on hyperbolic surfaces that themselves are degenerating, and this fact turns out to be essential for applications to the Teichmüller harmonic map flow.

This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by [Sar06] based on a random rotation followed by uniform column sampling. The result follows from a matrix version of Bernstein’s inequality and a tail inequality for quadratic forms in subgaussian random vectors.

In this paper we prove an analogue of Mordell’s inequality for lattices in finite-dimensional complex or quaternionic Hermitian space that are modules over a maximal order in an imaginary quadratic number field or a totally definite rational quaternion algebra. This inequality implies that 16dimensional Barnes-Wall lattice has optimal density among all 16-dimensional lattices with Hurwitz struc...

This paper addressed the robust stabilization performance of Takagi–Sugeno (T-S) fuzzy systems under a state feedback controller. To attain this, an integral inequality is proposed by rearranging quadratic matrix-vector form combined with Jensen’s to handle single terms obtained taking derivative concerned Lyapunov–Krasovskii functional. By employing this and using techniques, some improved del...

In this paper, quadratic stability of adaptive dynamic surface control for a class of nonlinear systems in strict-feedback form is analyzed in the framework of linear matrix inequality. While the existence of controller gains and filter time constants for semi-global stability was theoretically proved in the literature, it is not sufficient to describe how a set-point value and parameter update...

In this paper we propose a smoothing Newton-type algorithm for the problem of minimizing a convex quadratic function subject to finitely many convex quadratic inequality constraints. The algorithm is shown to converge globally and possess stronger local superlinear convergence. Preliminary numerical results are also reported.