An interior multiobjective primal-dual linear programming algorithm using approximated gradients and sequential generation of anchor points

::An algorithm for addressing multiple objective linear programming (MOLP) problems is presented. The algorithm modifies the path-following primal-dual algorithm to MOLP problems by using the singleobjective algorithm to generate interior search directions and later combine them to derive a single direction along which to step to the next iterate. Combining the different interior search directions is done by interacting with a Decision Maker (DM) to obtain locally-relevant preference information for the value vectors along these directions. This preference information is then used to derive an approximation to the gradient of an implicitly-known utility function, and using a projection of this gradient provides a direction vector along which we step to the next iterate. At each iteration the algorithm also generates boundary points that aid in deriving the combined search direction. We refer to these boundary points, generated sequentially during the process, as anchor points that serve as candidate solutions at which to terminate the iterative process.