A bstract We perform the ADM decomposition of a five-parameter family quadratic non-metricity theories and study their conjugate momenta. After systematically identifying all possible conditions which can be imposed on parameters such that different sets primary constraints arise, we find five-parametric theory space compartmentalized into nine sectors, based presence or absence constraints. Th...

Uncertainty theory is a branch of axiomatic mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. And uncertain variable is a fundamental concept in uncertainty theory which is used to represent imprecise quantities. This paper proposes a definition of quadratic entropy to characterize the uncertainty of uncertain variables resulting fr...

We consider the unrelated parallel machines scheduling problem where jobs have earliness and tardiness penalties and a common due date. We formulate this problem and some of its variants as 0-1 programs with quadratic objective function subject to linear constraints. The main contribution of this paper is to use and develop different convex reformulations to solve exactly the quadratic programs...

We study the quadratic resource allocation problem and its variant with lower upper constraints on nested sums of variables. This occurs in many applications, particular battery scheduling within decentralized energy management (DEM) for smart grids. present an algorithm this that runs $O(n \log n)$ time and, contrast to existing algorithms problem, achieves complexity using relatively simple e...

A method is presented to analyze the stability of feedback systems with neural network controllers. Two theorems are given prove asymptotic and compute an ellipsoidal innerapproximation region attraction (ROA). The first theorem addresses linear time-invariant systems, merges Lyapunov theory local (sector) quadratic constraints bound nonlinear activation functions in network. second allows syst...

We consider three parametric relaxations of the 0-1 quadratic programming problem. These relaxations are to: quadratic maximization over simple box constraints, quadratic maximization over the sphere, and the maximum eigenvalue of a bordered matrix. When minimized over the parameter, each of the relaxations provides an upper bound on the original discrete problem. Moreover, these bounds are eec...

Herein is investigated the method of solution of quadratic programming problems. The algorithm is based on the effective selection of constraints. Quadratic programming with constraintsequalities are solved with the help of an algorithm, so that matrix inversion is avoided, because of the more convenient organization of the Calculus. Optimal solution is determined in a finite number of iteratio...

We present an algorithm that achieves superlinear convergence for nonlinear programs satisfying the Mangasarian-Fromovitz constraint qualiication and the quadratic growth condition. This convergence result is obtained despite the potential lack of a locally convex augmented Lagrangian. The algorithm solves a succession of subproblems that have quadratic objective and quadratic constraints, both...