We consider the problem of estimating a density function that is known in advance to be convex. The maximum likelihood estimator is then the solution of a linearly constrained convex minimization problem. This problem turns out to be numerically difficult. We show that interior point algorithms perform well on this class of optimization problem, though for large samples numerical difficulties a...

We consider a supply function equilibrium (SFE) model of interaction in an electricity market. We assume a linear demand function and consider a competitive fringe and several strategic players having capacity limits and affine marginal costs. The choice of SFE over Cournot equilibrium and other models and the choice of affine marginal costs is reviewed in the context of the existing literature...

Motivated by problems in radio channel assignment, we consider the vertexlabelling of graphs with nonnegative integers. The objective is to minimize the span of the labelling, subject to constraints imposed at graph distances one and two. We show that the minimum span is (up to rounding) a piecewise linear function of the constraints, and give a complete specification, together with the associa...

Although artificial neural networks have shown great promise in applications including computer vision and speech recognition, there remains considerable practical and theoretical difficulty in optimizing their parameters. The seemingly unreasonable success of gradient descent methods in minimizing these non-convex functions remains poorly understood. In this work we offer some theoretical guar...

Abstract. We consider 3-monotone approximation by piecewise polynomials with prescribed knots. A general theorem is proved, which reduces the problem of 3-monotone uniform approximation of a 3-monotone function, to convex local L1 approximation of the derivative of the function. As the corollary we obtain Jackson-type estimates on the degree of 3-monotone approximation by piecewise polynomials ...

In this paper, we address a preemptive scheduling problem involving multiple nonreversible energy sources. To the classical scheduling issue, an additional decision level is added regarding the selection of the energy source used to satisfy the total power demand of tasks processed at each instant. Different non-reversible energy sources are available, with different characteristics in terms of...

Abstract Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds subsets vector spaces compositionally. It has been used model various application domains, from signal-flow graphs Petri nets and electrical circuits. In this paper, we introduce the its most expressive member date: Piecewise-Linear Algebra, new language specify piecewise-linear sp...