This paper first proposes a trust region algorithm to obtain a stationary point of unconstrained multiobjective optimisation problem. Under suitable assumptions, the global convergence of the new algorithm is established. We then extend the trust region method to solve the non-smooth multiobjective optimisation problem. [ABSTRACT FROM PUBLISHER]
In this paper, we consider an extension of ordinary linear programming (LP) that adds weighted logarithmic barrier terms for some variables. The resulting problem generalizes both LP and the problem of finding the weighted analytic centre of a polytope. We show that the problem has a dual of the same form and give complexity results for several different interior-point algorithms. We obtain an improved complexity result for certain cases by utilizing a combination of the volumetric and logarithmic barriers. As an application, we consider the complexity of solving the Eisenberg–Gale formulation of a Fisher equilibrium problem with linear utility functions. [ABSTRACT FROM PUBLISHER]
The solution of multidimensional Lipschitz optimization problem requires a lot of computing time and memory resources. Parallel OpenMP and MPI versions of branch and bound algorithm with simplicial partitions and Lipschitz bounds were created, investigated and compared in this paper. The efficiency of the developed parallel algorithms is investigated by solving multidimensional test problems for global optimization. [ABSTRACT FROM AUTHOR]
Detection of copositivity plays an important role in combinatorial and quadratic optimization. Recently, an algorithm for copositivity detection by simplicial partition has been proposed. In this paper, we develop an improved depth-first simplicial partition algorithm which reduces memory requirements significantly and therefore enables copositivity checks of much larger matrices - of size up to a few thousands instead of a few hundreds. The algorithm has been investigated experimentally on a number of MaxClique problems as well as on generated random problems. We present numerical results showing that the algorithm is much faster than a recently published linear algebraic algorithm for copositivity detection based on traditional ideas - checking properties of principal sub-matrices. We also show that the algorithm works very well for solving MaxClique problems through copositivity checks. [ABSTRACT FROM AUTHOR]