Bundle methods are often the algorithms of choice for nonsmooth convex optimization, especially if accuracy in the solution and reliability are a concern. We review several algorithms based on the bundle methodology that have been developed recently and that, unlike their forerunner variants, have the ability to provide exact solutions even if most of the … Read more
The risk parity optimization problem aims to find such portfolios for which the contributions of risk from all assets are equally weighted. Portfolios constructed using risk parity approach are a compromise between two well-known diversification techniques: minimum variance optimization approach and the equal weighting approach. In this paper, we discuss the problem of finding portfolios … Read more
We examine three primal space local Hoelder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations. Equivalent metric characterizations of the three mentioned regularity properties as well as a sufficient condition of [q]-subregularity in terms of Frechet normals are established. The relationships between [q]-regularity … Read more
We provide a formula for variational quasi-Newton updates with multiple weighted secant equations. The derivation of the formula leads to a Sylvester equation in the correction matrix. Examples are given. CitationReport naXys-09-2013, Namur Centre for Complex Systems, Unibersity of Namur, Namur (Belgium)ArticleDownload View PDF
We generalize the notions of user equilibrium and system optimum to non-atomic congestion games with stochastic demands. We establish upper bounds on the price of anarchy for three different settings of link cost functions and demand distributions, namely, (a) affine cost functions and general distributions, (b) polynomial cost functions and general positive-valued distributions, and (c) … Read more
Motivated by optimization considerations, we consider special Bishop-Phelps cones in R^n which are of the form {(t,x): t \geq ||x||} for some norm on R^(n-1). We show that for n bigger than 2, such cones are always irreducible. De fining the Lyapunov rank of a proper cone K as the dimension of the Lie algebra of … Read more
A new method for solving sequences of quadratic programs (QPs) is presented. For each new QP in the sequence, the method utilizes hot-starts that employ information computed by an active-set QP solver during the solution of the first QP. This avoids the computation and factorization of the full matrices for all but the first problem … Read more
We give an efficient algorithm for computing a Cournot equilibrium when the producers are confined to integers, the inverse demand function is linear, and costs are quadratic. The method also establishes existence, which follows in much more generality because the problem can be modelled as a potential game. CitationSchool of Operations Research and Information Engineering, … Read more
We consider the information relaxation approach for calculating performance bounds for stochastic dynamic programs (DPs), following Brown, Smith, and Sun (2010). This approach generates performance bounds by solving problems with relaxed nonanticipativity constraints and a penalty that punishes violations of these nonanticipativity constraints. In this paper, we study DPs that have a convex structure and … Read more
In linear classifiers, such as the Support Vector Machine (SVM), a score is associated with each feature and objects are assigned to classes based on the linear combination of the scores and the values of the features. Inspired by discrete psychometric scales, which measure the extent to which a factor is in agreement with a … Read more