On the reduced-set pareto-lipschitzian optimization

On the Pareto-Lipschitzian Optimization

A well-known example of global optimization that provides solutions within fixed error limits is optimization of functions with a known Lipschitz constant. In many real-life problems this constant is unknown. To address that, we propose a novel method called Pareto Lipshitzian Optimization (PLO) that provides solutions within fixed error limits for functions with unknown Lipschitz constants. In...

On the Pareto Optimality in the Context of Lipschitzian Optimization

A well-known example of global optimization that provides solutions within fixed error limits is optimization of functions with a known Lipschitz constant. In many real-life problems this constant is unknown. To address that, we propose a novel method called Pareto–Lipschitzian Optimization (PLO) that provides solutions within fixed error limits for functions with unknown Lipschitz constants. I...

On Pareto Set Generation in Multi-criteria Portfolio Optimization

Pareto set generation methods are considered with respect to their application for multi criteria portfolio selection. Several such methods were compared experimentally including some recently proposed evolutionary methods and the method of adjustable weights. Test problems were based on standard portfolio quality criteria and data on stocks of 10 Lithuanian companies. The experimental data on ...

Approximating the Pareto optimal set using a reduced set of objective functions

On Constrained Boolean Pareto Optimization

Pareto optimization solves a constrained optimization task by reformulating the task as a bi-objective problem. Pareto optimization has been shown quite effective in applications; however, it has little theoretical support. This work theoretically compares Pareto optimization with a penalty approach, which is a common method transforming a constrained optimization into an unconstrained optimiza...