New embeddings for nonlinear multiobjective optimization problems I

In a dialogue procedure the decision maker has to determine in each step the aspiration and reservation level expressing his wishes (goals). This leads to an optimization problem which is not easy to solve in the nonconvex case (the known starting point is not feasible). We propose a modified standard embedding (one parametric optimization). This problem will be discussed from the point of view of parametric optimization (non-degenerate critical points, singularities, pathfollowing methods to describe numerically a connected component in the set of stationary points and in the set of generalized critical points, respectively, and jumps (descent methods) to other connected components in these sets). This embedding is much better for computing a goal realizer or replaying that the goal was not realistic than the embeddings considered in the literature before, but in the worst case we have to find all connected components and this is an open problem.