Research Initiation:  Projective Methods for Global         Optimization of Quadratic Programs
{'Code': '05010200', 'Directorate': {'Abbreviation': 'CSE', 'LongName': 'Direct For Computer & Info Scie & Enginr'}, 'Division': {'Abbreviation': 'CCF', 'LongName': 'Division of Computing and Communication Foundations'}}
{'SignBlockName': 'S. Kamal Abdali', 'PO_EMAI': None, 'PO_PHON': None}
It is proposed to study extensions of Karmarkar's algorithm to global           optimization of quadratic programs.  Quadratic Feasibility over Simplex         (QFS) refers to the problem of determining if a given quadratic form            attains the value of zero over a simplex.  This problem is fundamental          to quadratic programming.  Our feasibility algorithm, which is                  essentially an algorithm for QFS with a positive semidefinite form,             consists of repeating the following steps: calculation of a "good"              descent direction for an appropriately defined potential (barrier)              function based on optimization over a circumscribing sphere, a line             search for the potential function, and centralization using a                   projective transformation.  It is proposed to generalize this approach          to the indefinite case.  Despite the NP-hardness of the indefinite              case, the convergence of this approach in general for some special              cases (even in worst-case exponential time) would result in an                  alternate algorithm for nonconvex programming which is expected to be           competitive with those which, in the worst-case, are of exponential             time and space complexity.  Having studied convergence, it is planned           to investigate computational approaches for such a procedure.  As an            alternate method for the calculation of descent direction, feasible             direction methods with projective transformation will be investigated.          It is also planned to study the effectiveness of projective algorithms          within our earlier methods for nonconvex quadratic programs which               require repeated application of a linear or convex quadratic                    programming algorithm.  Finally, the implementation of the resulting            algorithms using parallel architectures, such as NCUBE10 or ETA10               supercomputers, is planned.
{'FirstName': 'Bahman', 'LastName': 'Kalantari', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Bahman Kalantari', 'EmailAddress': 'kalantari@cs.rutgers.edu', 'NSF_ID': '000333769', 'StartDate': '09/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Rutgers University New Brunswick', 'CityName': 'NEW BRUNSWICK', 'ZipCode': '089018559', 'PhoneNumber': '8489320150', 'StreetAddress': '3 RUTGERS PLZ', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New Jersey', 'StateCode': 'NJ', 'CONGRESSDISTRICT': '12', 'CONGRESS_DISTRICT_ORG': 'NJ12', 'ORG_UEI_NUM': 'M1LVPE5GLSD9', 'ORG_LGL_BUS_NAME': 'RUTGERS, THE STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '2865', 'Text': 'NUMERIC, SYMBOLIC & GEO COMPUT'}
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