We consider a non-stationary sequential stochastic optimization problem, in which the underlying cost functions change over time under a variation budget constraint. We propose an $L_{p,q}$-variation functional to quantify the change, which yields less variation for dynamic function sequences...

Our concern lies in solving the following convex optimization problem: minimize cx subject to Ax=b, x \in P, where P is a closed convex set. We bound the complexity of computing an almost-optimal solution of this problem in terms of natural geometry-based measures of the feasible region and the...

Ever since the introduction of Markowitz's classical quadratic programming problem, transforming portfolio optimization into a linear programming (LP) problem has drawn much attention from researchers and practitioners, given the tractability of LP. However, using non-linear risk measures and...