Global optimization in problems with uncertainties

Problems with uncertainties can be viewed and formalized making use Of mult ifunctions or general set-valued functions which are usually non-differenti able. A new concept of global optimality is proposed which allows Lis to so lve global optimization problems with uncertainties, in natural setting Wit hout imposing artificial constraints oil uncertainties, nor introducing a k ind of partial ordering (in order to apply conventional optimality concepts and optimization techniques), nor considering solution, much less than in probability much greater than. With the new concept, deterministic optimiza tion requires two optimization procedures. Preliminary study Of the Subject is presented with many illustrative examples. Then. a monotonic iterative algorithm is developed which renders approximate solutions with a precision specified ill advance.(1).