Description
When solutions returned by PDLP and IPM (without crossover) are assessed by HiGHS, residual errors in the primal and dual equations are absorbed by changing the values of primal and dual slacks. Primal residual errors are then "measured" by primal infeasibilities that are as small as the residual errors. However, when residual corrections shift the value of primal variables off their bounds sufficiently, the corresponding dual value should be zero. However, if the dual value was meaningful because the primal variable was on (or close to) its bound - which is OK since the primal-dual objective difference (AKA complementarity) was OK - then this shows up as a large dual value.
Solutions returned by PDLP and IPM (without crossover) should not be changed by HiGHS, at the expense of introducing new measures (primal/dual residual errors by which their validity can be assessed by users.