相关论文: Truncation Dimension for Linear Problems on Multiv…
This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most $k$ non-zero components. We propose a simple yet effective solution called truncated power method that can…
We study the complexity of the classic capacitated k-median and k-means problems parameterized by the number of centers, k. These problems are notoriously difficult since the best known approximation bound for high dimensional Euclidean…
In this work we study weighted total least squares problems on infinite dimensional spaces. We show that in most cases this problem does not admit a solution (except in the trivial case) and then, we consider a regularization on the…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
The paper focuses on a multidimensional optimization problem, which is formulated in terms of tropical mathematics and consists in minimizing a nonlinear objective function subject to linear inequality constraints. To solve the problem, we…
A conventional linear model for functional data involves expressing a response variable $Y$ in terms of the explanatory function $X(t)$, via the model: $Y=a+\int_I b(t)X(t)dt+\hbox{error}$, where $a$ is a scalar, $b$ is an unknown function…
We consider the possible consistent truncation of N-extended supergravities to lower N' theories. The truncation, unlike the case of N-extended rigid theories, is non trivial and only in some cases it is sufficient just to delete the extra…
Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…
In the framework of abstract linear inverse problems in infinitedimensional Hilbert space we discuss generic convergence behaviours of approximate solutions determined by means of general projection methods, namely outside the standard…
Constructing active sets is a key part of the Multivariate Decomposition Method. An algorithm for constructing optimal or quasi-optimal active sets is proposed in the paper. By numerical experiments, it is shown that the new method can…
Let $f(x)$ be a real function which has $(n+1)$-th derivative on an interval $[a, b]$. For any point $x_0\in (a, b)$ and any integer $0\leq k\leq n$, denote by $S_{k,x_0}(x)$ the $k$-th truncation of the Taylor expansion of $f(x)$ at $x_0$,…
The problem of multivariate exponential analysis or sparse interpolation has received a lot of attention, especially with respect to the number of samples required to solve it unambiguously. In this paper we show how to bring the number of…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
We study QPT (quasi-polynomial tractability) in the worst case setting for linear tensor product problems defined over Hilbert spaces. We assume that the domain space is a reproducing kernel Hilbert space so that function values are well…
The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
In this paper, we establish a neural network to approximate functionals, which are maps from infinite dimensional spaces to finite dimensional spaces. The approximation error of the neural network is $O(1/\sqrt{m})$ where $m$ is the size of…
Squared error loss remains the most commonly used loss function for constructing a Bayes estimator of the parameter of interest. However, it can lead to sub-optimal solutions when a parameter is defined in a restricted space. It can also be…
The recently introduced $\{k\}$-packing function problem is considered in this paper. Special relation between a case when $k=1$, $k\ge 2$ and linear programming relaxation is introduced with sufficient conditions for optimality. For…
Given a strictly convex multiobjective optimization problem with objective functions $f_1,\dots,f_N$, let us denote by $x_0$ its solution, obtained as minimum point of the linear scalarized problem, where the objective function is the…