A linear programming (LP) based method is proposed for learning from experimental data in solving the nonlinear regression and classification problems. LP controls both the number of basis functions in a neural network (i.e., support vector machine) and the accuracy of learning machine. Two different methods are suggested in regression and their equivalence is discussed. Examples of function ap...

In this lecture, the focus is on general perfect matching problem where the goal is to prove that it can be solved in polynomial time by linear programming. Based on the LP formulation for bipartite matching studied in Lecture 10, we add some valid inequalities to establish a new formulation. Then we prove that for general perfect matching, all vertex solutions of the linear program are integra...

This paper presents a linear programming approach for the optimal control of nonlinear switched systems where the control is the switching sequence. This is done by introducing modal occupation measures, which allow to relax the problem as a primal linear programming (LP) problem. Its dual linear program of HamiltonJacobi-Bellman inequalities is also characterized. The LPs are then solved numer...

In this paper we present the theory and practice of co-logic programming (co-LP for brevity), a paradigm that combines both inductive and coinductive logic programming. Co-LP is a natural generalization of logic programming and coinductive logic programming, which in turn generalizes other extensions of logic programming, such as infinite trees, lazy predicates, and concurrent communicating pre...

Although addressing many of the same problems, the fields of Artificial Intelligence (AI) and Operations Research (OR) were seemingly developed independent of each other. Only recently has an effort been made to collaborate between the two in order to design smarter and faster algorithms. By merging the mathematical programming techniques of OR and the inference and/or randomized methods used i...

Linear programming is a very powerful tool for attacking hard combinatorial optimization problems. Methods such as the ellipsoid algorithm have shown that linear programming is solvable in polynomial time. Linear programming also plays a central role in the design of approximation algorithms. In fact, it is known that linear programming is P-complete, and this implies that if NP = P then for ev...

In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications include underdetermined Sparse Component Analysis (SCA), atomic decomposition on overcomplete dictionaries, compressed sensing, and decoding real field codes. Cont...

For many of us, modern-day linear programming (LP) started with the work of George Dantzig in 1947. However, it must be said that many other scientists have also made seminal contributions to the subject, and some would argue that the origins of LP predate Dantzig’s contribution. It is matter open to debate [36]. However, what is not open to debate is Dantzig’s key contribution to LP computatio...

We present an approach based on linear programming (LP) that estimates the weights for a pairwise comparison matrix generated within the framework of the analytic hierarchy process. Our approach makes sense for a number of reasons, which we discuss. We apply our LP approach to several sample problems and compare our results to those produced by other, widely used methods. In addition, we extend...

In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications include underdetermined Sparse Component Analysis (SCA), atomic decomposition on overcomplete dictionaries, compressed sensing, and decoding real field codes. Cont...