Automated analysis of convexity properties of nonlinear programs.

摘要

Many problems arising in engineering and other fields have been recognized as convex problems. The implications are many, perhaps the most important being that convex problems can be solved efficiently and globally. Knowing that a given problem is convex has therefore many useful practical implications, and we would expect that one of the first steps in analyzing a given problem would be to check for its convexity properties. The goal of this thesis is to develop an algorithm for identifying convexity of nonlinear optimization problems described in an algebraic way. We introduce the concept of estimators and develop an algorithm that has, among others, the following features: It is completely automated, it proves (when it succeeds) that the given problem is convex, and it is capable in some cases of transforming a non-convex problem into an equivalent convex one.