An improved algorithm for L2-Lp minimization problem

In this paper we consider a class of non-Lipschitz and non-convex minimization problems which generalize the L2−Lp minimization problem. We propose an iterative algorithm that decides the next iteration based on the local convexity/concavity/sparsity of its current position. We show that our algorithm finds an epsilon-KKT point within O(log(1/epsilon)) iterations. The same result is also … Read more

Multiperiod Multiproduct Advertising Budgeting: Stochastic Optimization Modeling

We propose a stochastic optimization model for the Multiperiod Multiproduct Advertising Budgeting problem, so that the expected profit of the advertising investment is maximized. The model is a convex optimization problem that can readily be solved by plain use of standard optimization software. It has been tested for planning a realistic advertising campaign. In our … Read more

A regularized limited-memory BFGS method for unconstrained minimization problems

The limited-memory BFGS (L-BFGS) algorithm is a popular method of solving large-scale unconstrained minimization problems. Since L-BFGS conducts a line search with the Wolfe condition, it may require many function evaluations for ill-posed problems. To overcome this difficulty, we propose a method that combines L-BFGS with the regularized Newton method. The computational cost for a … Read more

Optimizing healthcare network design under reference pricing and parameter uncertainty

Healthcare payers are exploring cost-containing policies to steer patients, through qualified information and financial incentives, towards providers offering the best value proposition. With Reference Pricing (RP), a payer or insurer determines a maximum amount paid for a procedure, and patients who select a provider charging more pay the difference. In a Tiered Network (TN), providers … Read more

Bounds on the stability number of a graph via the inverse theta function

In the paper we consider degree, spectral, and semide finite bounds on the stability number of a graph. The bounds are obtained via reformulations and variants of the inverse theta function, a notion recently introduced by the author in a previous work. Article Download View Bounds on the stability number of a graph via the inverse … Read more

On the Value Function of a Mixed Integer Linear Optimization Problem and an Algorithm for its Construction

This paper addresses the value function of a general mixed integer linear optimization problem (MILP). The value function describes the change in optimal objective value as the right-hand side is varied and understanding its structure is central to solving a variety of important classes of optimization problems. We propose a discrete representation of the MILP … Read more

A Generalization of Benders’ Algorithm for Two-Stage Stochastic Optimization Problems With Mixed Integer Recourse

We describe a generalization of Benders’ method for solving two-stage stochastic linear optimization problems in which there are both continuous and integer variables in the first and second stages. Benders’ method relies on finding effective lower approximations for the value function of the second-stage problem. In this setting, the value function is a discontinuous, non-convex, … Read more

Coercive polynomials and their Newton polytopes

Many interesting properties of polynomials are closely related to the geometry of their Newton polytopes. In this article we analyze the coercivity on $\mathbb{R}^n$ of multivariate polynomials $f\in \mathbb{R}[x]$ in terms of their Newton polytopes. In fact, we introduce the broad class of so-called gem regular polynomials and characterize their coercivity via conditions imposed on … Read more

Global Optimization via Slack Variables

This paper presents a method for finding global optima to constrained nonlinear programs via slack variables. The method only applies if all functions involved are of class C1 but without any further qualification on the types of constraints allowed; it proceeds by reformulating the given program into a bi-objective program that is then solved for … Read more

A Branch-and-Bound Algorithm for Instrumental Variable Quantile Regression

This paper studies a statistical problem called instrumental variable quantile regres- sion (IVQR). We model IVQR as a convex quadratic program with complementarity constraints and—although this type of program is generally NP-hard—we develop a branch-and-bound algorithm to solve it globally. We also derive bounds on key vari- ables in the problem, which are valid asymptotically … Read more