Methods of Optimization Under Uncertainty

摘要

Research under this grant has focused on large-scale optimization methodologyconnected with the solution of problems in which decisions must be made in the face of uncertainty: stochastic programming problems. The principal techniques developed for modeling such problem have been used various new kinds of decomposition into small-scale optimization problems in extended linear-quadratic programming. Extended linear-quadratic programming goes beyond ordinary linear and quadratic programming in allowing for objective functions to incorporate penalty terms and other features which create piecewise linear or quadratic formulas. The new decomposition techniques include primal-dual Lagrangian decomposition and forward-backward splitting. In total, four-year grant supported the writing of 16 technical papers (12 already in print or about to be the development and documentation of 2 computer codes, and the completion of 3 doctoral dissertations.... Large-scale optimization, Stochastic programming, Decision-making under uncertainty.