Knowledge-Based Linear Programming

We introduce a class of linear programs with constraints in the form of implications. Such linear programs arise in support vector machine classification, where in addition to explicit datasets to be classified, prior knowledge such as expert’s experience in the form of logical implications, are imposed on the classifier. The overall problem can be viewed either as a semi-infinite linear program or as a linear program with equilibrium constraints which, in either case, can be solved by an equivalent simple linear program under mild assumptions.