LP plays a special role in optimization theory: in one sense, it is a continuous optimization problem (first optimization problem) because the decision variables are real numbers, but it also may be considered a combinatorial optimization problem to identify an optimal basis containing certain columns from the constraint matrix (second optimization problem).

As a case study, we describe a novel transformation from clausal form Conjunctive Normal Form Satisfaction problem (CNF-SAT) to an integer linear programming model. The resulting matrix has a regular structure and is no longer problem-specific. It depends just on the number of clauses and the number of variables, but not on the structure of the clauses.

The structure of the integer program allows to solve it by means of standard linear programming techniques.

Then we describe several connectionist network paradigms to solve the second optimization problem. Some of these networks are effective in solving this problem as shown in significant tests.

The connectionist approach is compared with a standard Linear Programming (LP) procedure, and with a more recent hybrid LP technique.

A performance summary and final comments show the usefulness of the neural network proposal.