A new pragmatic approach to solve the problems of vector optimization with uncertain parameters

In this paper, we consider the method for solving problems of multi-criteria optimization with mathematical models that contain a lot of variables. The values of these variables are not regulated by a decision-maker. We introduce a new concept of 'tolerance of the decision variant'. This concept is similar to such concepts as stability, survivability, etc

On automatic tuning of basis functions in Bezier method

A transition from the fixed basis in Bezier's method to some class of base functions is proposed. A parameter vector of a basis function is introduced as additional information. This achieves a more universal form of presentation and analytical description of geometric objects as compared to the non-uniform rational B-splines (NURBS). This enables control of basis function parameters including control points, their weights and node vectors. This approach can be useful at the final stage of constructing and especially local modification of compound curves and surfaces with required differential and shape properties; it also simplifies solution of geometric problems. In particular, a simple elimination of discontinuities along local spline curves due to automatic tuning of basis functions is demonstrated