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In the past two decades nonlinear programming has matured a great deal. Today many design methodologies are employing some type of automated optimization to assist their design evaluation process. However, experience in large scale nonlinear programming algorithms still lags far behind that achieved in linear programming. In this work, the design of a general purpose large scale nonlinear programming algorithm is investigated.
The resulting algorithm is based on extensions to the generalized reduced gradient (GRG) method for solving the general nonlinear programming problem. The algorithm design presented represents the adoption of efficient methods for sparse matrices within the framework of the GRG algorithm. Additionally, techniques for resolving degeneracy, singularity and reducing constraint calculations are described.
A set of large scale nonlinear programming problems is developed based on the minimum weight design of three dimensional structures. The resulting implementation, LGOPT, was applied to three test problems. The results demonstrated that the algorithm was robust and would generally reach the solution in 10 iterations or less.