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We study the problem of approximation of 2D set of points. Such type of problems always occur in physical experiments, econometrics, data analysis and other areas. The often problems of outliers or spikes usually make researchers to apply…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…
This work is concerned with the formulation of a general framework for the analysis of meshfree approximation schemes and with the convergence analysis of the Local Maximum-Entropy (LME) scheme as a particular example. We provide conditions…
Trigonometric polynomials are usually defined on the lattice of integers.We consider the larger class of weight and root lattices with crystallographic symmetry.This article gives a new approach to minimize trigonometric polynomials, which…
The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities by reducing to polynomial inequalities. Finally, we show the great applicability of this algorithm and as examples, we use it to…
This paper studies the hierarchy of local minimums of a polynomial in the space. For this purpose, we first compute H-minimums, for which the first and second order optimality conditions are satisfied. To compute each H-minimum, we…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
We derive a new adaptive leverage score sampling strategy for solving the Column Subset Selection Problem (CSSP). The resulting algorithm, called Adaptive Randomized Pivoting, can be viewed as a randomization of Osinsky's recently proposed…
We consider the problem of maximizing the revenue raised from tolls set on the arcs of a transportation network, under the constraint that users are assigned to toll-compatible shortest paths. We first prove that this problem is strongly…
Multivariate polynomial optimization is a prevalent model for a number of engineering problems. From a mathematical viewpoint, polynomial optimization is challenging because it is non-convex. The Lasserre's theory, based on semidefinite…
This work proposes an efficient parallel algorithm for non-monotone submodular maximization under a knapsack constraint problem over the ground set of size $n$. Our algorithm improves the best approximation factor of the existing parallel…
Width-based search algorithms seek plans by prioritizing states according to a suitably defined measure of novelty, that maps states into a set of novelty categories. Space and time complexity to evaluate state novelty is known to be…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…
We present theoretical guarantees for an alternating minimization algorithm for the dictionary learning/sparse coding problem. The dictionary learning problem is to factorize vector samples $y^{1},y^{2},\ldots, y^{n}$ into an appropriate…
The classical Artin--Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequivalent absolute values. Several variants and generalizations…
Let $\A$ be a free arrangement of $d$ lines in the complex projective plane, with exponents $d_1\leq d_2$. Let $m$ be the maximal multiplicity of points in $\A$. In this note, we describe first the simple cases $d_1 \leq m$. Then we study…
This paper deals with the optimization of Bolza problem with a system of convex and nonconvex, discrete and differential state variable inequality constraints of second order by deriving necessary and sufficient conditions for optimality.…
We present a polynomial-time $\frac{3}{2}$-approximation algorithm for the problem of finding a maximum-cardinality stable matching in a many-to-many matching model with ties and laminar constraints on both sides. We formulate our problem…
In this paper we demonstrate that a well known linear inequality method developed for rational Chebyshev approximation is equivalent to the application of the bisection method used in quasiconvex optimisation. Although this correspondence…
In this paper, we study the optimal general convergence rates for quadratures derived from Chebyshev points. By building on the aliasing errors on integration of Chebyshev polynomials, together with the asymptotic formulae on the…