joint work with Shinji Mizuno, Jianming Shi
This research concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We show that the problem is equivalent to a mixed integer programming (MIP) problem, and we propose to compute an optimal solution by solving the MIP problem. Compared with the previous mixed integer programming approach, the proposed approach relaxes a condition for the multiobjective linear programming problem and reduces the size of the MIP problem. The MIP problem can be efficiently solved by current MIP solvers when the objective function is convex or linear.
joint work with Stefano Lucidi, Giampaolo Liuzzi, Veronica Piccialli
Solving a global optimization problem is a hard task. We define recursive non-linear equations that are able to transform the variables space and allow us to tackle the problem in an advantageous way. The idea is to exploit the information obtained during a multi-start approach in order to define a sequence of transformations in the variables space. The aim is that of expanding the basin of attraction of global minimizers while shrinking those of already found local minima.
In this paper, we propose a procedure for listing KKT points of a quadratic reverse convex programming problem (QRC) whose feasible set is expressed as the area excluded the interior of a convex set from another convex set. Since it is difficult to solve (QRC), we transform (QRC) into a parametric quadratic programming problem~(QP). In order to solve (QP) for each parameter, we introduce an algorithm for listing KKT points. Moreover, we propose an global optimization algorithm for (QRC) by incorporating our KKT listing algorithm into a parametric optimization method.