  We study a class of non-convex sum-of-ratios programs which can be used for
decision-making in prominent areas such as product assortment and price
optimization, facility location, and security games. Such an optimization
problem involves both continuous and binary decision variables and is known to
be highly non-convex and intractable to solve. We explore a discretization
approach to approximate the optimization problem and show that the approximate
program can be reformulated as mixed-integer linear or second-order cone
programs, which can be conveniently handled by an off-the-shelf solver (e.g.,
CPLEX or GUROBI). We further establish (mild) conditions under which solutions
to the approximate problem converge to optimal solutions as the number of
discretization points increases. We also provide approximation abounds for
solutions obtained from the approximated problem. We show how our approach
applies to product assortment and price optimization, maximum covering facility
location, and Bayesian Stackelberg security games and provide experimental
results to evaluate the efficiency of our approach.
