this paper analyzes a controllable discrete-time machine repair problem withl operating machines and two repairmen. the number of working servers can be adjusteddepending on the number of failed machines in the system one at a time at machine's failure orat service completion epochs. analytical closed-form solutions of the stationary probabilities ofthe number of failed machines in the sys...

In this paper, line search based on Sequential Quadratic Programming is implemented in order to find a solution to Fuzzy Relation Equations. Sequential Quadratic Programming is a gradient-based method that uses a quadratic estimation of the objective function in each iteration’s neighborhood. Unlike analytical approaches, the method can handle equations with any combinations of t-norms and t-co...

We completely solve the family of relative Thue equations x − (t − 1)xy − (t + 2)xy − y = μ, where the parameter t, the root of unity μ and the solutions x and y are integers in the same imaginary quadratic number field. This is achieved using the hypergeometric method for |t| ≥ 53 and Baker’s method combined with a computer search using continued fractions for the remaining values of t.

We completely solve the family of relative Thue equations x − (t − 1)xy − (t+ 2)xy − y = μ, where the parameter t, the root of unity μ and the solutions x and y are integers in the same imaginary quadratic number field. This is achieved using the hypergeometric method for |t| ≥ 53 and Baker’s method combined with a computer search using continued fractions for the remaining values of t.

This paper presents the rank minimization approach to solve general bilinear matrix inequality (BMI) problems. Due to the NP-hardness of BMI problems, no proposed algorithm that globally solves general BMI problems is a polynomial-time algorithm. We present a local search algorithm based on the semidefinite programming (SDP) relaxation approach to indefinite quadratic programming, which is anal...

A natural damping of Newton's method for nonsmooth equations is presented. This damping, via the path search instead of the traditional line search, enlarges the domain of convergence of Newton's method and therefore is said to be globally convergent. Convergence behavior is like that of line search damped Newton's method for smooth equations, including Q-quadratic convergence rates under appro...

The minimization of a convex quadratic function under bound constraints is a fundamental building block for solving more complicated optimization problems. The active-set method introduced by Bergounioux et al. [1, 2] has turned out to be a powerful, fast and competitive approach for this problem. Hintermüller et al. [15] provide a theoretical explanation of its efficiency by interpreting it as...

 This paper present unequal-sized facilities layout solutions generated by a genetic search program named LADEGA (Layout Design using a Genetic Algorithm). The generalized quadratic assignment problem requiring pre-determined distance and material flow matrices as the input data and the continuous plane model employing a dynamic distance measure and a material flow matrix are discussed. Computa...