For the classic problem of fair allocation of indivisible goods, we introduce the notion of minimum social inequality allocations and discuss its connection to other fair allocation rules such as minimum envy. We show that a fair allocation problem can always be cast as the problem of finding an...

We revisit the problem of minimizing a separable convex function with a linear constraint and box constraints. This optimization problem arises naturally in many applications in economics, insurance, and finance. Existing literature exclusively tackles this problem by using the traditional...

Let X1, . . . , Xn be a set of n continuous and non-negative random variables, with log-concave joint density function f, faced by a person who seeks for an optimal deductible coverage for this n risks. Let d = (d1, . . . dn) and d ∗ = (d ∗ 1 , . . . d∗ n ) be two vectors of deductibles...

We revisit the problem of minimizing a separable convex function with a linear constraint and box constraints. This optimization problem arises naturally in many applications in economics, insurance, and finance. Existing literature exclusively tackles this problem by using the traditional...