Simplex Algorithm

[ftneek]

The changes all seem good. I'm adding them to the source code.

Just so it's clear, simplex_core now requires canonical form to use while simplex2 allows for standard form input, correct? so simplex2==current simplex_core in source code, and changing the call to simplex2 + updating the output for the current tests should cause them to pass.

I thought you said in one comment that simplex_int would use the simplex() wrapper but I don't think I see that. That would require the equality constraints to be listed first right?

Last, how come you added the plane cutting algorithm again inside simplex_le? Can you not just use simplex_int inside simplex_le?

Albert Chan Wrote:In simplex_core(), it have 2 branch return no solution (P is total pivot1() calls)

RETURN ["No Solution: empty feasible region (w≠0)",a,bv,P,[]];
...
RETURN ["No Solution",a,bv,P,[]];

What is the difference?

The w!=0 check happens when the system has artificial variables and they have been zero'd out of the artificial w row.

The other return statement you are referencing happens during an iteration of dual simplex, and I think should be analogous to the check that happens in step 3. It is possible that the return statements could use a better description.

From my understanding here is what can happen:
X=optimal solution to primal <--> Y=optimal solution to dual
other possibilities:
Max is unbounded above and Dual Min with no feasible solutions
Min is unbounded below and Dual Max with no feasible solutions
Both with no feasible solutions

So I think the w!=0 check might correspond to the 3rd 'other possibility'