29 citations · 171 across the 24 of their papers we have counts for
24 papers
Characterization of Unique Solvability of Absolute Value Equations: An Overview, Extensions, and Future Directions
Shubham Kumar, Deepmala, Milan Hladik +1
This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic…
A Brief Review of Explainable Artificial Intelligence in Healthcare
Zahra Sadeghi, Roohallah Alizadehsani, Mehmet Akif Cifci +13
XAI refers to the techniques and methods for building AI applications which assist end users to interpret output and predictions of AI models. Black box AI applications in high-sta…
On unbounded directions of linear interval parametric systems and their extensions to AE solutions
M. Hladík
We consider a system of linear equations, whose coefficients depend linearly on interval parameters. Its solution set is defined as the set of all solutions of all admissible reali…
Error bounds and a condition number for the absolute value equations
Moslem Zamani, Milan Hladic
Absolute value equations, due to their relation to the linear complementarity problem, have been intensively studied recently. In this paper, we present error bounds for absolute v…
Computing the spectral decomposition of interval matrices and a study on interval matrix power
David Hartman, Milan Hladík, David Říha
We present an algorithm for computing a spectral decomposition of an interval matrix as an enclosure of spectral decompositions of particular realizations of interval matrices. The…
A class of optimization problems motivated by rank estimators in robust regression
Michal Cerny, Miroslav Rada, Jaromir Antoch +1
A rank estimator in robust regression is a minimizer of a function which depends (in addition to other factors) on the ordering of residuals but not on their values. Here we focus…
Stability of the linear complementarity problem properties under interval uncertainty
Milan Hladík
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity pr…
Regularity radius: Properties, approximation and a not a priori exponential algorithm
David Hartman, Milan Hladik
The radius of regularity sometimes spelled as the radius of nonsingularity is a measure providing the distance of a given matrix to the nearest singular one. Despite its possible a…
Interval Linear Programming under Transformations: Optimal Solutions and Optimal Value Range
Elif Garajová, Milan Hladík, Miroslav Rada
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data,…
Duality Gap in Interval Linear Programming
Jana Novotná, Milan Hladík, Tomáš Masařík
This paper deals with the problem of linear programming with inexact data represented by real closed intervals. Optimization problems with interval data arise in practical computat…
Testing weak optimality of a given solution in interval linear programming revisited: NP-hardness proof, algorithm and some polynomial cases
Miroslav Rada, Milan Hladík, Elif Garajová
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We di…
An Overview of Polynomially Computable Characteristics of Special Interval Matrices
Milan Hladík
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, t…
AE regularity of interval matrices
Milan Hladík
Consider a linear system of equations with interval coefficients, and each interval coefficient is associated with either a universal or an existential quantifier. The AE solution…
Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix
Milan Hladík
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of che…
Eigenvalues of symmetric tridiagonal interval matrices revisited
Milan Hladík
In this short note, we present a novel method for computing exact lower and upper bounds of eigenvalues of a symmetric tridiagonal interval matrix. Compared to the known methods, o…
Interval Linear Algebra and Computational Complexity
Jaroslav Horáček, Milan Hladík, Michal Černý
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singul…
Efficient Approaches for Enclosing the United Solution Set of the Interval Generalized Sylvester Matrix Equations
Marzieh Dehghani-Madiseh, Milan Hladík
In this work, we investigate the interval generalized Sylvester matrix equation and develop some techniques for obtaining outer estim…
Selection-based Approach to Cooperative Interval Games
Jan Bok, Milan Hladík
Cooperative interval games are a generalized model of cooperative games in which the worth of every coalition corresponds to a closed interval representing the possible outcomes of…
Robust optimal solutions in interval linear programming with forall-exists quantifiers
Milan Hladík
We introduce a novel kind of robustness in linear programming. A solution x* is called robust optimal if for all realizations of objective functions coefficients and constraint mat…
Efficient Solution of a Class of Quantified Constraints with Quantifier Prefix Exists-Forall
Milan Hladík, Stefan Ratschan
In various applications the search for certificates for certain properties (e.g., stability of dynamical systems, program termination) can be formulated as a quantified constraint…
On the Efficient Gerschgorin Inclusion Usage in the Global Optimization αBB Method
Milan Hladík
In this paper, we revisit the αBB method for solving global optimization problems. We investigate optimality of the scaling vector used in Gerschgorin's inclusion theorem to calcul…
A New Operator and Method for Solving Interval Linear Equations
Milan Hladík
We deal with interval linear systems of equations. We present a new operator, which generalizes the interval Gauss-Seidel method. Also, based on the new operator and properties of…
Subsquares Approach - Simple Scheme for Solving Overdetermined Interval Linear Systems
Jaroslav Horáček, Milan Hladík
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear sys…
Computing Enclosures of Overdetermined Interval Linear Systems
Jaroslav Horáček, Milan Hladík
This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval…