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Global optimization and singular nonlinear programs: New techniques (2009), submitted to the proceedings of SCAN

By Julie Roy and R. Baker Kearfott


We consider the general nonlinear program. Both linear and nonlinear programs are often approximately ill-posed, with an entire continuum of approximate optimizing points. As an example, we take a linear program derived from a simple investment scenario. In this problem, any point along the portion of a line is a solution to this problem. If we perturb the coefficients of this problem slightly, the resulting problem has a unique solution. However, the perturbed problem inherits a set of approximate solutions along a portion of the line. In both the exactly singular case and the approximately singular case, we obtain the parametric representation of the solution set (or the approximate solution set) from a singular value decomposition of the matrix of gradients of the objective and active constraints, although, in the approximately singular case, more constraints are active, and we need to explore by selectively removing some constraints to find directions in which feasibility is maintained. Although it can be practical to know, commercial software doesn’t always detect such manifolds of solutions. We report progress in this area

Topics: global optimization, singular nonlinear programs
Year: 2008
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