The investigator develops the theory for the generalnonlinear rescaling principle for constrained optimization. Based on this principle, he finds theoretically well-grounded and numerically efficient methods for solving large-scale constrained optimization problems. Constrained optimization problems arise in all areas ofscientific, technological, and commercial activities. The problem is to choose values of parameters, subject to certain limits on their values, so as to make some function of the parameters take on an extreme value. For instance, one might try to locate warehouses so as to minimize the costs of shipping items to individual distribution sites. Or one might choose the placement of structural members to maximize the strength of the structure subject to weight constraints. Problems like these can involve thousands of parameters and tens of thousands of constraints. The investigator develops and studies efficient and numerically stable methods for large-scale optimization problems. The ability to solve such problems is critical in optimal structural design, forecasting, network optimization, optimal control, economics, and finance communication problems.
