Csizmadia, Adrienn
Published in
Pure Mathematics and Applications

The traditional criss-cross algorithm for the linear programming problem is shown to be finite when s-monotone index selection rules are used. The set of s-monotone index selection rules, among others, include the Last In First Out (LIFO) and the Most Often Selected Variable rule (MOSV). The advantage of applying the s-monotone index selection rule...

Klatt, M Munk, A Zemel, Y

Abstract
We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. For the corresponding random linear program, we characterize under general assumptions the random fluctuations of the empirical optimal solutions around their population quantities after standardization by a dist...

Manucci, Mattia Aguado, Jose Vicente Borzacchiello, Domenico
Published in
Computational Methods in Applied Mathematics

This paper is concerned with the use of the focal underdetermined system solver to recover sparse empirical quadrature rules for parametrized integrals from existing data. This algorithm, originally proposed for image and signal reconstruction, relies on an approximated ℓ p {\ell^{p}} -quasi-norm minimization. Compared to ℓ 1 {\ell^{1}} -norm minim...

Akram, Muhammad Ullah, Inayat Allahviranloo, Tofigh
Published in
Computational and Applied Mathematics

In this study, we first show that the existing arithmetic operations of trapezoidal fuzzy numbers do not satisfy the basic properties. Then, for trapezoidal fuzzy numbers, we define new arithmetic operations. Furthermore, we demonstrate that the existing Simplex method for addressing fully fuzzy linear programming problems has some drawbacks. Final...

Abdullahi, Habibu Awasthi, A. K. Waziri, Mohammed Yusuf Halilu, Abubakar Sani
Published in
Computational and Applied Mathematics

As it is known that, not all conjugate gradient (CG) methods satisfy descent property, a necessary condition for attaining global convergence result. In this article, we propose three different sufficient-descent conjugate gradient projection algorithms for constrained monotone equations. Using Dai–Yuan (DY) conjugate gradient parameter, we generat...

Li, Guoyin Pong, Ting Kei
Published in
Foundations of Computational Mathematics

In this paper, we study the Kurdyka–Łojasiewicz (KL) exponent, an important quantity for analyzing the convergence rate of first-order methods. Specifically, we develop various calculus rules to deduce the KL exponent of new (possibly nonconvex and nonsmooth) functions formed from functions with known KL exponents. In addition, we show that the wel...

Yue, M-C Kuhn, D Wiesemann, W

Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate and solve data-driven optimization problems with rigorous statistical guarantees. In this techni...

Silva, Lino M. Oliveira, Aurelio R. L.
Published in
Computational and Applied Mathematics

The interior-point method solves large linear programming problems in a few iterations. Each iteration requires computing the solution to one or more linear systems. This constitutes the most expensive step of the method and reducing the time to solve these linear systems is a way of improving the method’s performance. Iterative methods such as the...

Sharma, Sanchita Arora, Shalini
Published in
International Journal of Applied and Computational Mathematics

This article explores a class of bi-objective capacitated transportation problem with bounds over the distribution capacity of origin points and requirement capacity of demand points. The concerned problem is converted into an equivalent balanced bi-objective transportation model with upper bound restrictions on the decision variables. The article ...

Akram, Muhammad Ullah, Inayat Allahviranloo, Tofigh Edalatpanah, S. A.
Published in
Computational and Applied Mathematics

There are several daily life problems where we have to deal with the uncertainties and we are forced to solve the uncertain linear programming models. Certain methods have been presented for dealing with linear programming problems based on fuzzy sets and intuitionistic fuzzy sets which are characterized by membership degree, membership and non-mem...