Yes, that is correct.  You can do it a little more simply by omitting the starting solution and the WITH NLP clause. ... View more

The FIX statement fixes variables to the specified values.  If you want to minimize the function, don't fix anything, and the solver will find optimal values for the variables.  At a locally optimal solution, the dual values will be 0.  But to find the gradient at a given solution, you must fix the variables.  The resulting dual values (gradient) indicate the direction of steepest descent.  As you did in other questions, you would proceed with a line search to find the best step length alpha in that direction. ... View more

That is correct.  You can also do: print x x.dual; ... View more

Your code looks correct to me, but you can do it a little more simply by omitting the SAVE QPS statement and the WITH QP clause and by including the bounds in the VAR statement: proc optmodel; var x{1..3} >= 0 <= 5; minimize f = x[1] - 2*x[2] + 4*x[3] + x[1]**2 + 2*x[2]**2 + 3*x[3]**2 + x[1]*x[2]; con r1: 3*x[1] + 4*x[2] -2*x[3] <= 10; con r2: -3*x[1] + 2*x[2] + x[3] >= 2; con r3: 2*x[1] + 3*x[2] + 4*x[3] =5; solve; print x; quit; By using the EXPAND / SOLVE statement, you can see that both versions pass the same formulation to the solver. ... View more

As described here, implicit variables are useful when the same expression is needed in several places and you don't want to increase the number of explicit variables and constraints. For your code, if you wanted to replace the first implicit variable, for example, it would look like this: *impvar AmountUsed {r in RESOURCES} = sum {p in PRODUCTS} NumProd[p] * required[p,r]; var AmountUsed {RESOURCES}; con AmountUsedCon {r in RESOURCES}: AmountUsed[r] = sum {p in PRODUCTS} NumProd[p] * required[p,r];   ... View more