Anti-optimization technique - a generalization of interval analysis for nonprobabilistic treatment of uncertainty

Anti-optimization technique, on the one hand, represents an alternative and complement to traditional probabilistic methods. and on the other hand. it is a generalization of the mathematical theory of interval analysis. In th is study, in terms of interval analysis or interval mathematics. the arithm etic operations and the partial order relation of anti-optimization techniq ue can be defined, and the convex model variables and the convex model exte nsion function of convex models can also be introduced. The comparison of t he Lagrange multiplier method with the convex model extension method for ev aluating the region of static displacements of structures with uncertain-bu t-bounded parameters shows that the width of the upper and lower bounds on the static displacement yielded by the Lagrange multiplier method of convex models is lighter than those produced by the convex model extension. (C) 2 001 Elsevier Science Ltd. All rights reserved.