Suppose I solve a linear programming problem with the simplex
algorithm, then change a row of coefficients. I then change the
previously found optimal basis slightly or not at all (by one or zero
variables -- both cases are relevant here) so that the new basis is
primal feasible. Given how little I changed from the first problem, it
seems that I should be able to solve a second one without having to
restart from scratch. Is this possible?
Yes. If you change a row, the optimal basic solution may either remain
optimal or become primal infeasible, but in both cases it remains dual
feasible, so you can reoptimize the modified lp with the dual simplex