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The new iteration methods for solving absolute value equations

Rashid Ali, Kejia Pan (2023)

Applications of Mathematics

Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations A x - | x | = b , where A ∈ ℝ n × n is an M -matrix or strictly diagonally dominant matrix, b ∈ ℝ n and x ∈ ℝ n is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness and effectiveness...

The nonlinear complementarity model of industrial symbiosis network equilibrium problem

Shiqin Xu, Guoshan Liu, Wendai Lv, Yingmei Liu (2014)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper, we propose an industrial symbiosis network equilibrium model by using nonlinear complementarity theory. The industrial symbiosis network consists of industrial producers, industrial consumers, industrial decomposers and demand markets, which imitates natural ecosystem by means of exchanging by-products and recycling useful materials exacted from wastes. The industrial producers and industrial consumers are assumed to be concerned with maximization of economic profits as well as minimization...

The optimization of heat radiation intensity

Mlýnek, Jaroslav, Srb, Radek (2013)

Programs and Algorithms of Numerical Mathematics

This article focuses on the problem of calculating the intensity of heat radiation and its optimization across the surface of an aluminium or nickel mould. The inner mould surface is sprinkled with a special PVC powder and the outer mould surface is warmed by infrared heaters located above the mould. In this way artificial leathers are produced in the car industry (e.g., the artificial leather on a car dashboard). The article includes a description of how a mathematical model allows us to calculate the...

The Orderly Colored Longest Path Problem – a survey of applications and new algorithms

Marta Szachniuk, Maria Cristina De Cola, Giovanni Felici, Jacek Blazewicz (2014)

RAIRO - Operations Research - Recherche Opérationnelle

A concept of an Orderly Colored Longest Path (OCLP) refers to the problem of finding the longest path in a graph whose edges are colored with a given number of colors, under the constraint that the path follows a predefined order of colors. The problem has not been widely studied in the previous literature, especially for more than two colors in the color arrangement sequence. The recent and relevant application of OCLP is related to the interpretation of Nuclear Magnetic Resonance experiments for...

The output least squares identifiability of the diffusion coefficient from an H 1 –observation in a 2–D elliptic equation

Guy Chavent, Karl Kunisch (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability. The analysis shows the influence of the flow direction on the parameter to be estimated. A scale analysis for multi-scale resolution of the unknown parameter is provided.

The Output Least Squares Identifiability of the Diffusion Coefficient from an H1–Observation in a 2–D Elliptic Equation

Guy Chavent, Karl Kunisch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability. The analysis shows the influence of the flow direction on the parameter to be estimated. A scale analysis for multi-scale resolution of the unknown parameter is provided.

The partial inverse minimum cut problem with L1-norm is strongly NP-hard

Elisabeth Gassner (2010)

RAIRO - Operations Research

The partial inverse minimum cut problem is to minimally modify the capacities of a digraph such that there exists a minimum cut with respect to the new capacities that contains all arcs of a prespecified set. Orlin showed that the problem is strongly NP-hard if the amount of modification is measured by the weighted L1-norm. We prove that the problem remains hard for the unweighted case and show that the NP-hardness proof of Yang [RAIRO-Oper. Res.35 (2001) 117–126] for this problem with additional bound...

The periodic Vehicle routing problem: classification and heuristic

M. Mourgaya, F. Vanderbeck (2006)

RAIRO - Operations Research

Periodic Vehicle Routing Problem: classification and heuristic for tactical planning. The Periodic Vehicle Routing Problem (PVRP) consists in assigning customer visits to vehicle routes in some periods of a time horizon so as to satisfy some service level requirements that can take the form of frequency of visit, constraint on time lag between visits, or pre-defined visit patterns. We present different variants of this problem and propose a classification. Then, we consider a model for tactical...

The Polytope of m-Subspaces of a Finite Affine Space

Julie Christophe, Jean-Paul Doignon (2007)

RAIRO - Operations Research

The m-subspace polytope is defined as the convex hull of the characteristic vectors of all m-dimensional subspaces of a finite affine space. The particular case of the hyperplane polytope has been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general m-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the...

The risk-sensitive Poisson equation for a communicating Markov chain on a denumerable state space

Rolando Cavazos-Cadena (2009)

Kybernetika

This work concerns a discrete-time Markov chain with time-invariant transition mechanism and denumerable state space, which is endowed with a nonnegative cost function with finite support. The performance of the chain is measured by the (long-run) risk-sensitive average cost and, assuming that the state space is communicating, the existence of a solution to the risk-sensitive Poisson equation is established, a result that holds even for transient chains. Also, a sufficient criterion ensuring that...

The second order optimality conditions for nonlinear mathematical programming with C 1 , 1 data

Liping Liu, Michal Křížek (1997)

Applications of Mathematics

To find nonlinear minimization problems are considered and standard C 2 -regularity assumptions on the criterion function and constrained functions are reduced to C 1 , 1 -regularity. With the aid of the generalized second order directional derivative for C 1 , 1 real-valued functions, a new second order necessary optimality condition and a new second order sufficient optimality condition for these problems are derived.

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