Convex optimization homework solution

The constraints, x 0, 1Tx = 1, are clearly convex, so we just need to show that the objective is concave (since it is to be maximized)

The basic problem can be expressed as This is a convex optimization problem since the objective is concave and the constraints are a set of linear inequalities

To transform it to an equivalent LP, we rst express the revenue functions as which holds since rj is concave

It follows that rj(xj) uj if and only if with variables x and u

(g) The set of points whose distance to a does not exceed a xed fraction of the distance to b, i

A slab is an intersection of two halfspaces, hence it is a convex set (and a polyhedron)