Mathematical Sciences:  Research in Optimal Control and     Optimization
{'Code': '03040100', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Michael Steuerwalt'}
Professor Warga is a prominent senior investigator who has made            many contributions to the theory of optimization.  In this project he           proposes to develop higher order conditions for optimality by applying a        new result called "Nonsmooth Open Mapping Principle".                                    The higher order necessary  conditions of optimality are used          to verify solutions obtained from the first order necessary conditions.         Sometimes the problem is mathematically degenerate and the first order          conditions provide no information on the nature of the optimal                  solutions.  In both cases, the second order conditions are useful.              Nonetheless, the development of general second order conditions is a            difficult mathematical problem.                                                          Professor Warga succeeded recently in developing such results          and intends to pursue this line of development.  The novelty and                difficulty of his approach is in the use of a nonconvex set of                  admissible variations.  This is the first time anyone has succeeded in          doing this.                                                                              Several other directions of work are described in this project:        optimal control problems with constraints imposed on the system's state,        differential games with nonadditively coupled controls,                         problems with delays, and computer implementation of theoretical                results.
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1986&All=true', 'xml': '8619002.xml'}