We focus on a permutation betting market under parimutuel call auction model where traders bet on the final ranking of n candidates. We present a Proportional Betting mechanism for this market. Our mechanism allows the traders to bet on any subset of the n x n ‘candidate-rank’ pairs, and rewards them proportionally to the number … Read more
The ballroom dancing showcases at Fred Astaire East Side Dance Studio in Manhattan are held at least twice a year and provide the students with an environment for socializing, practice, and improvement. The most important part of a showcase organization is the construction of the dance presentations timetable, and, with the number of participants increasing … Read more
We prove several inequalities on the determinants of sublattices in LLL-reduced bases. They generalize the fundamental inequalities of Lenstra, Lenstra, and Lovasz on the length of the shortest vector, and show that LLL-reduction finds not only a short vector, but also sublattices with small determinants. We also prove new inequalities on the product of the … Read more
In applications such as signal processing and statistics, many problems involve finding sparse solutions to under-determined linear systems of equations. These problems can be formulated as a structured nonsmooth optimization problems, i.e., the problem of minimizing L_1-regularized linear least squares problems. In this paper, we propose a block coordinate gradient descent method (abbreviated as CGD) … Read more
Value-at-Risk (VaR) is an integral part of contemporary financial regulations. Therefore, the measurement of VaR and the design of VaR optimal portfolios are highly relevant problems for financial institutions. This paper treats a VaR constrained Markowitz style portfolio selection problem when the distribution of returns of the considered assets are given in the form of … Read more
Citation This paper is published in Lecture Notes in Artificial Intelligence 5139, p411-418, Springer
We study general algorithmic frameworks for online learning tasks. These include binary classification, regression, multiclass problems and cost-sensitive multiclass classification. The theorems that we present give loss bounds on the behavior of our algorithms that depend on general conditions on the iterative step sizes. Citation International Journal of Pure and Applied Mathematics, Vol. 46 (2008), … Read more
We present a new algorithm, Iterative Estimation Maximization (IEM), for stochastic linear programs with Conditional Value-at-Risk constraints. IEM iteratively constructs a sequence of compact-sized linear optimization problems, and solves them sequentially to find the optimal solution. The problem size IEM solves in each iteration is unaffected by the size of random samples, which makes it … Read more
This paper is concerned with a scheduling problem that occurs in service systems, where customers are classified as `ordinary’ and `special’. Ordinary customers can be served on any service facility, while special customers can be served only on the flexible service facilities. Customers arrive dynamically over time and their needs become known upon arrival. We … Read more
We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy leaves enough user-flexibility but gives a mathematical guarantee for the algorithm’s behavior in … Read more