In this paper we propose a new simplicial partition-based deterministic algorithm for global optimization of Lipschitz-continuous functions without requiring any knowledge of the Lipschitz constant. Our algorithm is motivated by the well-known Direct algorithm which evaluates the objective function on a set of points that tries to cover the most promising subregions of the feasible region. Almo...

Explaining the excellent practical performance of the simplex method for linear programming has been a major topic of research for over 50 years. One of the most successful frameworks for understanding the simplex method was given by Spielman and Teng (JACM ‘04), who the developed the notion of smoothed analysis. Starting from an arbitrary linear program with d variables and n constraints, Spie...

An efficient exterior point simplex type algorithm for the assignment problem has been developed by Paparrizos [K. Paparrizos, An infeasible (exterior point) simplex algorithm for assignment problems, Math. Program. 51 (1991) 45–54]. This algorithm belongs to the category of forest algorithms and solves an n × n assignment problem in at most n(n−1) 2 iterations and in at most O(n3) time. In thi...

Aiming at the problem of cloud service selection based on global Quality-of-Service (QoS) constraints, this paper provides a hybrid algorithm of Simplex Method (SM) and Genetic Algorithm (GA). In this algorithm, some relevant variables are defined, some Simplex Method operations are proposed and the hybrid algorithm based on GA and SM is provided. The global convergence ability and local conver...

The fixed-cost Capacitated Multicommodity Network Design (CMND) problem is a well known NP-hard problem. This paper presents a matheuristic algorithm combining Simulated Annealing (SA) metaheuristic and Simplex method for CMND problem. In the proposed algorithm, a binary array is considered as solution representation and the SA algorithm manages open and closed arcs. Several strategies for open...

In a recent paper, Yang proposes an integer labeling algorithm for determining whether an arbitrary simplex P in R n contains an integer point or not. The problem under consideration is a very di cult one in the sense that it is NPcomplete. The algorithm is based on a speci c integer labeling rule and a speci c triangulation of R n . In this paper we discuss a practical implementation of the al...

The dual simplex algorithm has become a strong contender in solving large scale LP problems. One key problem of any dual simplex algorithm is to obtain a dual feasible basis as a starting point. We give an overview of methods which have been proposed in the literature and present new stable and efficient ways to combine them within a state-of-the-art optimization system for solving real world l...

In a recent primal-dual simplex-type algorithm [K. Paparrizos, N. Samaras and G. Stephanides, 2003, A new efficient primal dual simplex algorithm. Computers & Operations Research 30, 1383–1399], their authors show how to take advantage of the knowledge of a primal feasible point and they work with a square basis during the whole process. In this paper we address what could be thought of as its ...