  Ranking items to be recommended to users is one of the main problems in large
scale social media applications. This problem can be set up as a
multi-objective optimization problem to allow for trading off multiple,
potentially conflicting objectives (that are driven by those items) against
each other. Most previous approaches to this problem optimize for a single slot
without considering the interaction effect of these items on one another.
  In this paper, we develop a constrained multi-slot optimization formulation,
which allows for modeling interactions among the items on the different slots.
We characterize the solution in terms of problem parameters and identify
conditions under which an efficient solution is possible. The problem
formulation results in a quadratically constrained quadratic program (QCQP). We
provide an algorithm that gives us an efficient solution by relaxing the
constraints of the QCQP minimally. Through simulated experiments, we show the
benefits of modeling interactions in a multi-slot ranking context, and the
speed and accuracy of our QCQP approximate solver against other state of the
art methods.
