Robust Growth-Optimal Portfolios

The growth-optimal portfolio is designed to have maximum expected log-return over the next rebalancing period. Thus, it can be computed with relative ease by solving a static optimization problem. The growth-optimal portfolio has sparked fascination among finance professionals and researchers because it can be shown to outperform any other portfolio with probability 1 in the … Read more

Computationally tractable counterparts of distributionally robust constraints on risk measures

In optimization problems appearing in fields such as economics, finance, or engineering, it is often important that a risk measure of a decision-dependent random variable stays below a prescribed level. At the same time, the underlying probability distribution determining the risk measure’s value is typically known only up to a certain degree and the constraint … Read more

A new mixed integer linear programming formulation for one problem of exploration of online social networks

Enormous global popularity of online social network sites has initiated numerous studies and methods investigating different aspects of their use, so some concepts from network-based studies in optimization theory can be used for research into online networks. In Gaji\’c (2014) are given a several new mixed integer linear programming formulations for first and second problem … Read more

The constant objective value property for combinatorial optimization problems

Given a combinatorial optimization problem, we aim at characterizing the set of all instances for which every feasible solution has the same objective value. Our central result deals with multi-dimensional assignment problems. We show that for the axial and for the planar $d$-dimensional assignment problem instances with constant objective value property are characterized by sum-decomposable … Read more

Second-order cone programming approach for elliptically distributed joint probabilistic constraints with dependent rows

In this paper, we investigate the problem of linear joint probabilistic constraints. We assume that the rows of the constraint matrix are dependent and the dependence is driven by a convenient Archimedean copula. Further we assume the distribution of the constraint rows to be elliptically distributed, covering normal, $t$, or Laplace distributions. Under these and … Read more

A Novel Unified Approach to Invariance in Control

In this paper, we propose a novel, unified, general approach to investigate sufficient and necessary conditions under which four types of convex sets, polyhedra, polyhedral cones, ellipsoids and Lorenz cones, are invariant sets for a linear continuous or discrete dynamical system. In proving invariance of ellipsoids and Lorenz cones for discrete systems, instead of the … Read more

Application of the Strictly Contractive Peaceman-Rachford Splitting Method to Multi-block Separable Convex Programming

Recently, a strictly contractive Peaceman- Rachford splitting method (SC-PRSM) was proposed to solve a convex minimization model with linear constraints and a separable objective function which is the sum of two functions without coupled variables. We show by an example that the SC-PRSM cannot be directly extended to the case where the objective function is … Read more

Active-set prediction for interior point methods using controlled perturbations

We propose the use of controlled perturbations to address the challenging question of optimal active-set prediction for interior point methods. Namely, in the context of linear programming, we consider perturbing the inequality constraints/bounds so as to enlarge the feasible set. We show that if the perturbations are chosen appropriately, the solution of the original problem … Read more

Toward Scalable Stochastic Unit Commitment – Part 2: Solver Configuration and Performance Assessment

In this second portion of a two-part analysis of a scalable computational approach to stochastic unit commitment, we focus on solving stochastic mixed-integer programs in tractable run-times. Our solution technique is based on Rockafellar and Wets’ progressive hedging algorithm, a scenario-based decomposition strategy for solving stochastic programs. To achieve high-quality solutions in tractable run-times, we … Read more

Toward Scalable Stochastic Unit Commitment – Part 1: Load Scenario Generation

Unit commitment decisions made in the day-ahead market and during subsequent reliability assessments are critically based on forecasts of load. Traditional, deterministic unit commitment is based on point or expectation-based load forecasts. In contrast, stochastic unit commitment relies on multiple load scenarios, with associated probabilities, that in aggregate capture the range of likely load time-series. … Read more