Separable Programming J.PELFORT

When crossproducts appear Xi*Xj a change of variables could be always made to obtain separability again . The integer solution of the former problem is restrained to be 0,1,2,3 sorry i forgot mention the number 3. And the solution [3,0,0,0] is not optimal but it is interesting in its own way, why? Note that when applying any cutting plane method to solve the LAP the integer solution coincides with the solution of a standard Continuos SIMPLEX ( No cutting planes are added) this is due to the fact that the point we have obtained is a vertex of its convex hull. The continuos approximation can be obtained with sample [0.2, 0.4 , 0.6, 0.8, 1, 1.2, 1.5 ] To know more in Separable Programming please read : RR Meyer - ‎1979 - ‎ abr. 1979 - New iterative separable programming techniques based on two-segment, piecewise-linear approximations are described for the minimization of convex separable functions over convex sets. These techniques have two advantages over traditional separable programming methods. The first is that they do not require the cumbersome “fine grid” approximations employed to achieve high accuracy in the usual separable programming approach. In addition, the new methods yield feasible solutions with objective values guaranteed to be within any specified tolerance of optimality. In computational tests with real-world problems of up to 500 “nonlinear” variables the approach has exhibited rapid convergence and yielded very close bounds on the optimal value. Paper No. P-383, April (1953); 15. C.E. Miller. The SIMPLEX method for local separable programming, Standard Oil Company of California, San Francisco (1960). Report of the Electronic Computer Center August. 16. I.B. PyneLinear programming on an electronic analogue computer. AIEE Trans. Ann. (1956), pp. 139-143.