In economic and engineering application of mathematics sometimes we need to optimize more than one objective function at the same time. In this type of problems we need to find solutions, where one of the objectives can not be improved without worsen the other. These solutions are called Pareto-optimal solutions, and since 1950's such methods are known to compute one of the Pareto-optimal solutions.
Recently, for unconstrained multi objective optimization problems such algorithm has been developed by Oliver Schütze at al. (2003) that try to approximate the whole set of the Pareto-optimal solutions. In this talk we generalize the subdivision algorithm of Schütze and others for linearly constrained multi objective optimization problem. The objective functions in our case need to be differentiable convex functions. The main idea of the method to find feasible joint decreasing direction, for the objective functions. Further generalization of the more general class of problems (convex constrained and convex objective function for mineralization problem) seems to be possible. Practical applicability of the new algorithm has tested on the Markowitz portfolio optimization problem.
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