COMMENT TO THE ARTICLE 'SEVERAL EXAMPLES OF APPLICATION OF NASH AND PARETO APPROACHES TO MULTIOBJECTIVE STRUCTURAL OPTIMIZATION WITH UNCERTAINTIES' OF N. V. BANICHUK, F. RAGNEDDA, M. SERRA

摘要

The authors of the article "Several Examples of Application of NASH and PARETO Approaches to Multiobjective Structural Optimization with Uncertainties" confirm that the PARETO and NASH formulations lead the identical PARETO and NASH fronts. We examine these solutions from the viewpoint of inequalities theory and reveal the mathematical sense of the discovered PARETO and NASH fronts. The general conjecture could be formulated as follows. Consider multiobjective optimization problem involving more than one objective functionals to be optimized simultaneously. If a relation between objective functionals, which could be expressed in terms of an isoperimetric inequality, exists, then the PARETO and NASH fronts coincide and emerge as the equality case of the isoperimetric inequality.