We discuss two models from the literature that have been developed to formulate piecewise linear approximations of separable nonlinear functions by way of mixed-integer programs. We show that the most commonly proposed method is computationally inferior to a lesser known technique by comparing analytically the linear programming relaxations of the two formulations. A third way of formulating th...

It has been shown in a number of recent papers that Graver bases methods enable to solve linear and nonlinear integer programming problems in variable dimension in polynomial time, resulting in a variety of applications in operations research and statistics. In this article we continue this line of investigation and show that Graver bases also enable tominimize quadratic and higher degree polyn...

This paper investigates inexact Uzawa methods for nonlinear saddle point problems. We prove that the inexact Uzawa method converges globally and superlinearly even if the derivative of the nonlinear mapping does not exist. We show that the Newton-type decomposition method for saddle point problems is a special case of a Newton-Uzawa method. We discuss applications of inexact Uzawa methods to se...

The Quadratic Convex Reformulation (QCR) method is used to solve quadratic unconstrained binary optimization problems. In this method, the semidefinite relaxation is used to reformulate it to a convex binary quadratic program which is solved using mixed integer quadratic programming solvers. We extend this method to random quadratic unconstrained binary optimization problems. We develop a Penal...

Today, billions of smart devices are interconnected via wireless networks, leading to large volumes video contents circulating through the bandwidth-limited backhaul. This causes network performance deteriorate. As a mitigation mechanism, caching highly popular edges is deployed. We propose cooperative and demand-aware strategy, which modelled using Separable Assignment Problem, maximize cache ...

A new active set algorithm for minimizing quadratic functions with separable convex constraints is proposed by combining the conjugate gradient method with the projected gradient. It generalizes recently developed algorithms of quadratic programming constrained by simple bounds. A linear convergence rate in terms of the Hessian spectral condition number is proven. Numerical experiments, includi...

We consider the linearly constrained separable convex programming whose objective function is separable into m individual convex functions with non-overlapping variables. The alternating direction method (ADM) has been well studied in the literature for the special case m = 2. But the convergence of extending ADM to the general case m ≥ 3 is still open. In this paper, we show that the straightf...

Given a multi-dimensional Markov diffusion X, the Malliavin integration by parts formula provides a family of representations of the conditional expectation E[g(X2)|X1]. The different representations are determined by some localizing functions. We discuss the problem of variance reduction within this family. We characterize an exponential function as the unique integratedvariance minimizer amon...

We develop an approximation algorithm for a dynamic capacity allocation problem with Markov modulated customer arrival rates. For each time period and each state of the modulating process, the algorithm approximates the dynamic programming value function using a concave function that is separable across resource inventory levels. We establish via computational experiments that our algorithm inc...

An answer set program with variables is first-order definable on finite structures if the set of its finite answer sets can be captured by a first-order sentence. Characterizing classes of programs that are first-order definable on finite structures is theoretically challenging and of practical relevance to Answer Set Programming. In this paper, we identify a non-trivial class of answer set pro...