We show that the saturation order of piecewise constant approximation in Lp norm on convex partitions with N cells is N −2/(d+1), where d is the number of variables. This order is achieved for any f ∈ W 2 p (Ω) on a partition obtained by a simple algorithm involving an anisotropic subdivision of a uniform partition. This improves considerably the approximation order N−1/d achievable on isotropi...

This paper addresses the problem of capturing nondominated points on convex Pareto frontiers, which are encountered in invex multi-objective programming problems. An algorithm to find a piecewise linear approximation of the nondominated set of convex Pareto frontier are applied. Index Term-Approximation, Nondominated points, Invex multi-objective problems, Block norms.

We give an algorithm to compute a morph between any two convex drawings of the same plane graph. The morph preserves the convexity of the drawing at any time instant and moves each vertex along a piecewise linear curve with linear complexity. The linear bound is asymptotically optimal in the worst case. 1998 ACM Subject Classification G.2.2. Graph Theory

Piecewise linear maps over triangulations are used extensively in geometric modelling and computer graphics. This short note surveys recent progress on the important question of when such maps are one-to-one, central to which are convex combination maps.

This paper considers a particular class of dynamic robust optimization problems, where a large number of decisions must be made in the first stage, which consequently fix the constraints and cost structure underlying a one-dimensional, linear dynamical system. We seek to bridge two classical paradigms for solving such problems, namely, (1) dynamic programming (DP), and (2) policies parameterize...

We present two partitioning algorithms that allow a sum of piecewise linear polynomials over a number of overlaying convex partitions of the unit cube Ω in Rd to approximate a function f ∈ W 3 p (Ω) with the order N−6/(2d+1) in Lp-norm, where N is the total number of cells of all partitions, which makes a marked improvement over the N−2/d order achievable on a single convex partition. The gradi...

In this paper, by examining the recession properties of convex polynomials, we provide a necessary and sufficient condition for a piecewise convex polynomial to have a Hölder-type global error bound with an explicit Hölder exponent. Our result extends the corresponding results of [25] from piecewise convex quadratic functions to piecewise convex polynomials.

We propose an Economic Probabilistic analogy: the category of cost is analogous to the category of Probability. The proposed analogy permits construction of an informal theory of nonlinear non-convex Gaussian Utility and Cost, which describes the real economic processes more adequately than a theory based on a linear and convex models. Based on the proposed analogy, we build a nonlinear non-con...

In this paper an approach based on evolutionary algorithms to find Pareto optimal pair of state and control for multi-objective optimal control problems (MOOCP)'s is introduced‎. ‎In this approach‎, ‎first a discretized form of the time-control space is considered and then‎, ‎a piecewise linear control and a piecewise linear trajectory are obtained from the discretized time-control space using ...

We describe a detailed computational procedure which, given data values at arbitrarily distributed points in the plane, determines if the data are convex and, if so, constructs a smooth convex surface that interpolates the data. The method consists of constructing a triangulation of the nodes (data abscissae) for which the triangle-based piecewise linear interpolant is convex, computing a set o...