By adding slack variables, equations in this process can be converted into aug-
The criss-cross and ellipsoid algorithms are methods for doing this process, for which Khachiyan developed the  rst polynomial-time algorithm. Karmakar's al- gorithm, a highly e cient algorithm for this process, is an interior point method. By adding slack variables, equations in this process can be converted into aug- mented form, allowing the application of the simplex algorithm, which operates by moving between the vertices of the   feasible region until it  nds the solu- tion. For ten points, identify this process by which a linear function of several variables is optimized over a region constrained by several inequalities.
The criss-cross and ellipsoid algorithms are methods for doing this process, for which Khachiyan developed the  rst polynomial-time algorithm.
linear programming