| Abstract: |
| The well-known Karush-Kuhn-Tucker (KKT) Theorem provides a set of necessary conditions for a local minimum point subject to finitely many inequality/equality constraints. This long term research project is to develop computational theory and methods for finding multiple KKT points in an infinite-dimensional space setting. In Part 1, an equivalent condition is established for a KKT point, from which a numerical method can be devised to compute a KKT point as a constrained local minimum point. This method is mathematically validated. Numerical examples will be presented to illustrate the algorithm. By an implementation strategy, a convergence result is established. It turns out that this equivalent condition opens a door for people to design numerical methods for computing multiple KKT points or solutions to some differential inclusion problems. |
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