Modeling of Competition and Collaboration Networks under Uncertainty: Stochastic Programs with Resource and Bilevel

We analyze stochastic programming problems with recourse characterized by a bilevel structure. Part of the uncertainty in such problems is due to actions of other actors such that the considered decision maker needs to develop a model to estimate their response to his decisions. Often, the resulting model exhibits connecting constraints in the leaders (upper-level) subproblem. It is shown that this problem can be formulated as a new class of stochastic programming problems with equilibrium constraints (SMPEC). Sufficient optimality conditions are stated. A solution algorithm utilizing a stochastic quasi-gradient method is proposed, and its applicability extensively explained by practical numerical examples

Functional Bipartite Ranking: a Wavelet-Based Filtering Approach

It is the main goal of this article to address the bipartite ranking issue from the perspective of functional data analysis (FDA). Given a training set of independent realizations of a (possibly sampled) second-order random function with a (locally) smooth autocorrelation structure and to which a binary label is randomly assigned, the objective is to learn a scoring function s with optimal ROC curve. Based on linear/nonlinear wavelet-based approximations, it is shown how to select compact finite dimensional representations of the input curves adaptively, in order to build accurate ranking rules, using recent advances in the ranking problem for multivariate data with binary feedback. Beyond theoretical considerations, the performance of the learning methods for functional bipartite ranking proposed in this paper are illustrated by numerical experiments

Advances in Polynomial Optimization

Polynomial optimization has a wide range of practical applications in fields such as optimal control, energy and water networks, facility location, management science, and finance. It also generalizes relevant optimization problems thoroughly studied in the literature, such as mixed-binary linear optimization, quadratic optimization, and complementarity problems. As finding globally optimal solutions is an extremely challenging task, the development of efficient techniques for solving polynomial optimization problems is of particular relevance. In this thesis we provide a detailed study of different techniques to solve this kind of problems and we introduce some nobel approaches in this field, including the use of statistical learning techniques. Furthermore, we also present a practical application of polynomial optimization to finance and more specifically, portfolio design

Robust optimization methods for chance constrained, simulation-based, and bilevel problems

The objective of robust optimization is to find solutions that are immune to the uncertainty of the parameters in a mathematical optimization problem. It requires that the constraints of a given problem should be satisfied for all realizations of the uncertain parameters in a so-called uncertainty set. The robust version of a mathematical optimization problem is generally referred to as the robust counterpart problem. Robust optimization is popular because of the computational tractability of the robust counterpart for many classes of uncertainty sets, and its applicability in wide range of topics in practice. In this thesis, we propose robust optimization methodologies for different classes of optimization problems. In Chapter 2, we give a practical guide on robust optimization. In Chapter 3, we propose a new way to construct uncertainty sets for robust optimization using the available historical data information. Chapter 4 proposes a robust optimization approach for simulation-based optimization problems. Finally, Chapter 5 proposes approximations of a specific class of robust and stochastic bilevel optimization problems by using modern robust optimization techniques

Time and Location Aware Mobile Data Pricing

Mobile users' correlated mobility and data consumption patterns often lead to severe cellular network congestion in peak hours and hot spots. This paper presents an optimal design of time and location aware mobile data pricing, which incentivizes users to smooth traffic and reduce network congestion. We derive the optimal pricing scheme through analyzing a two-stage decision process, where the operator determines the time and location aware prices by minimizing his total cost in Stage I, and each mobile user schedules his mobile traffic by maximizing his payoff (i.e., utility minus payment) in Stage II. We formulate the two-stage decision problem as a bilevel optimization problem, and propose a derivative-free algorithm to solve the problem for any increasing concave user utility functions. We further develop low complexity algorithms for the commonly used logarithmic and linear utility functions. The optimal pricing scheme ensures a win-win situation for the operator and users. Simulations show that the operator can reduce the cost by up to 97.52% in the logarithmic utility case and 98.70% in the linear utility case, and users can increase their payoff by up to 79.69% and 106.10% for the two types of utilities, respectively, comparing with a time and location independent pricing benchmark. Our study suggests that the operator should provide price discounts at less crowded time slots and locations, and the discounts need to be significant when the operator's cost of provisioning excessive traffic is high or users' willingness to delay traffic is low.Comment: This manuscript serves as the online technical report of the article accepted by IEEE Transactions on Mobile Computin