Details

Autor(en) / Beteiligte

• LEVY, Adam B

Titel

Solution sensitivity from general principles

Ist Teil von

• SIAM journal on control and optimization, 2001-01, Vol.40 (1), p.1-38

Ort / Verlag

Philadelphia, PA: Society for Industrial and Applied Mathematics

Erscheinungsjahr

2001

Quelle

EBSCOhost Business Source Ultimate

Beschreibungen/Notizen

• We present a generic approach for the sensitivity analysis of solutions to parameterized finite-dimensional optimization problems. We study differentiability and continuity properties of quasi-solutions (stationary points or stationary point-multiplier pairs), as well as their existence and uniqueness, and the issue of when quasi-solutions are actually optimal solutions. Our approach is founded on a few general rules that can all be viewed as generalizations of the classical inverse mapping theorem, and sensitivity analyses of particular optimization models can be made by computing certain generalized derivatives in order to translate the general rules into the terminology of the particular model. The useful application of this approach hinges on an inverse mapping theorem that allows us to compute derivatives of solution mappings without computing solutions, which is crucial since numerical solutions to sensitive problems are fundamentally unreliable. We illustrate how this process works for parameterized nonlinear programs, but the generality of the rules on which our approach is based means that a similar sensitivity analysis is possible for practically any finite-dimensional optimization problem. Our approach is distinguished not only by its broad applicability but by its separate treatment of different issues that are frequently treated in tandem. In particular, meaningful generalized derivatives can be computed and continuity properties can be established even in cases of multiple or no quasi-solutions (or optimal solutions) for some parameters. This approach has not only produced unprecedented and computable conditions for traditional properties in well-studied situations, but has also characterized interesting new properties that might otherwise have remained unexplored.