Related papers: D\"orfler marking with minimal cardinality is a li…
We consider problems to make a given bidirected graph strongly connected with minimum cardinality of additional signs or additional arcs. For the former problem, we show the minimum number of additional signs and give a linear-time…
Cardinality constraints in optimization are commonly of $L^0$-type, and they lead to sparsely supported optimizers. An efficient way of dealing with these constraints algorithmically, when the objective functional is convex, is…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…
Providing explanations about how machine learning algorithms work and/or make particular predictions is one of the main tools that can be used to improve their trusworthiness, fairness and robustness. Among the most intuitive type of…
Cardinality-constrained diameter partitioning asks for a partition of $n$ items into two classes of prescribed sizes that minimizes the larger of the two class diameters. We give an $O(n^2)$ algorithm and a matching $\Omega(n^2)$ lower…
Dealing with multi-objective problems by using generation methods has some interesting advantages since it provides the decision-maker with the complete information about the set of non-dominated points (Pareto front) and a clear overview…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
Many real-world combinatorial problems involve uncertain parameters, which can be predicted given contextual features and historical data. These `predict-then-optimize' or `contextual optimization' problems have gained significant…
Trimming is a ubiquitous operation in computer-aided-design whereby parts of a geometry are merged, intersected, or simply discarded. While it grants virtually unlimited flexibility in geometric design, it introduces a plethora of other…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
We consider a matching problem in a bipartite graph $G=(A\cup B,E)$ where nodes in $A$ are agents having preferences in partial order over their neighbors, while nodes in $B$ are objects without preferences. We propose a polynomial-time…
Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of…
Index tracking is a popular passive investment strategy aimed at optimizing portfolios, but fully replicating an index can lead to high transaction costs. To address this, partial replication have been proposed. However, the cardinality…
Sequential minimum optimization is a machine-learning global search training algorithm. It is applicable when the functional dependence of the cost function on a tunable parameter given the other parameters can be cheaply determined. This…
In this paper we address cardinality estimation problem which is an important subproblem in query optimization. Query optimization is a part of every relational DBMS responsible for finding the best way of the execution for the given query.…
This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of…