Ordering problems assign weights to each ordering and ask to find an ordering of maximum weight. We consider problems where the cost function is either linear or quadratic. In the first case, there is a given profit if the element u is before v in the ordering. In the second case, the profit depends on whether u is before v and r is before s. The linear ordering problem is well studied, with ex...

The Economic Dispatch Problem (EDP) is one of the important optimization problem in a power system. Traditionally, in EDP, the cost function for each generator has been approximately represented by a single quadratic function. The main aim of EDP is to minimize the total cost of generating real power while satisfying the equality constraints of power balance and the inequality generator capacit...

In this paper we describe an Interior Point Method (IPM) to solve large scale NonLinear Programming (NLP) problems, tailored to the solution of a specialized Optimal Power Plow (OPF) formulation that uses bus voltages in rectangular coordinates. The distinctive feature of this OPF formulation is that the objective function and constraints are quadratic functions, and such quadratic properties a...

In the present paper, a linear parabolic evolution equation is considered whose bilinear form is controlled from a general Banach space. The control-to-state operator and some important properties thereof are presented. For a quadratic objective function, the gradient in the control space is derived. A-posteriori error estimators are presented for a given reduced-order model (ROM) with respect ...

In recent years, analysts and policy makers alike have been evaluating the nexus between exchange rates and macroeconomic stability. Among the most important questions asked is why have some countries adopted rigid, including fixed, exchange-rate regimes, while others have opted for more flexible systems? This paper addresses this question from a political economy perspective, both theoreticall...

The ability of velocity methods to describe changes of topology by creating defects like holes is investigated. For the shape optimization energy-type objective functions are considered, which depend on the geometry by means of state variables. The state system is represented by abstract, quadratic, constrained minimization problems stated over domains with defects. The velocity method provides...

A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under L2 norm but with less segmentation. The re-parameterization functions we used are C continuous piecewise rational linear functions, which provide more flexibility and can b...

Valiant’s (2007) model of evolvability models the evolutionary process of acquiring useful functionality as a restricted form of learning from random examples. Linear threshold functions and their various subclasses, such as conjunctions and decision lists, play a fundamental role in learning theory and hence their evolvability has been the primary focus of research on Valiant’s framework (2007...

Let Y (t) be a stochastic process on [0; 1] modeled as dYt = (t)dt + dW (t), where W (t) denotes a standard Wiener process, and (t) is an unknown function assumed to belong to a given set L2[0; 1]. We consider the problem of estimating the value L( ), where L is a known continuous linear function de ned on , using linear estimators of the form hm; yi = R m(t)dY (t); m 2 L2[0; 1]. We solve the p...

In the present paper we outline the stochastic limit approach to superfluidity. The Hamiltonian describing the interaction between the Bose condensate and the normal phase is introduced. Sufficient in the stochastic limit condition of superfluidity is proposed. Existence of superfluidity in the stochastic limit of this system is proved and the non– linear (quadratic) equation of motion describi...