In conservation planning, the data related to size, growth and diffusion of populations is sparse, hard to collect and unreliable at best. If and when the data is readily available, it is not of sufficient quantity to construct a probability distribution. In such a scenario, applying deterministic or stochastic approaches to the problems in conservation … Read more
In this paper, we consider the basic problem of portfolio construction in financial engineering, and analyze how market-based and analytical approaches can be combined to obtain efficient portfolios. As a first step in our analysis, we model the asset returns as a random variable distributed according to a mixture of normal random variables. We then … Read more
The general formulation for finding the L1-norm best-fit subspace for a point set in $m$-dimensions is a nonlinear, nonconvex, nonsmooth optimization problem. In this paper we present a procedure to estimate the L1-norm best-fit one-dimensional subspace (a line through the origin) to data in $\Re^m$ based on an optimization criterion involving linear programming but which … Read more
This paper studies the vehicle routing problem with time windows and multiple deliverymen in which customer demands are uncertain and belong to a predetermined polytope. In addition to the routing decisions, this problem aims to define the number of deliverymen used to provide the service to the customers on each route. A new mathematical formulation … Read more
We give explicit solutions for utility optimization problems in the presence of Knightian uncertainty in continuous time with nondominated priors and finite time horizon in a diffusion model. We assume that the uncertainty set is compact and time dependent on $[0,T]$. We solve the robust optimization problem explicitly both when the investor’s utility is of … Read more
This paper examines the impacts of governmental incentives for coal-fired power plants to generate renewable energy via biomass cofiring technology. The most common incentive is the production tax credit (PTC), a flat rate reimbursement for each unit of renewable energy generated. The work presented here proposes PTC alternatives, incentives that are functions of plant capacity … Read more
Stochastic user equilibrium models are fundamental to the analysis of transportation systems. Such models are typically developed under the assumption of route based choice models for the users. A class of link based models under a Markovian assumption on the route choice behavior of the users has been proposed to deal with the drawbacks of … Read more
This paper is concerned with the rank constrained optimization problem whose feasible set is the intersection of the rank constraint set $\mathcal{R}=\!\big\{X\in\mathbb{X}\ |\ {\rm rank}(X)\le \kappa\big\}$ and a closed convex set $\Omega$. We establish the local (global) Lipschitzian type error bounds for estimating the distance from any $X\in \Omega$ ($X\in\mathbb{X}$) to the feasible set and … Read more
We reformulate the zero-norm minimization problem as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the complementarity constraint to the objective, is exact. Then, by the special structure of the exact penalty problem, we propose a decomposition method that can seek a global optimal solution of the … Read more
This article analyzes how the Unit Commitment Problem (UCP) complexity evolves with respect to the number n of units and T of time periods.A classical reduction from the knapsack problem shows that the UCP is NP-hard in the ordinary sense even for T=1. The UCP is proved to be strongly NP-hard.When either a unitary cost … Read more