Parametric Optimization: Singularities, Pathfollowing and Jumps

Part 1 Introduction: a preliminary survey on solution algorithms in one-parametric optimization some motivations abstracts of the chapters 2-6. Part 2 Theoretical background: unconstrained optimization problems constraint sets critical points, stationary points, stability generic singularities in one-parametric optimization problems the approach via piecewise differentiability. Part 3 Pathfollowing of curves of local minimizers: the estimation of the radius of convergence an active index set strategy the ALGORITHM PATH I and numerical results. Part 4 Pathfollowing along a connected component in the Karush-Kuhn-Tucker set and in the critical set: pathfollowing in the Karush-Kuhn-Tucker set the ALGORITHM PATH II and numerical results pathfollowing in the critical set the ALGORITHM PATH III. Part 5 Pathfollowing in the set of local minimizers and in the set of critical points: jumps in the set of local minimizers and the ALGORITHM JUMP I jumps in the critical set and the ALGORITHM JUMP II. Part 6 Applications: on globally convergent algorithms on global optimization on multiobjective optimization.