A parsimonious model for generating arbitrage-free scenario trees

Simulation models of economic, financial and business risk factors are widely used to assess risks and support decision-making. Extensive literature on scenario generation methods aims at describing some underlying stochastic processes with the least number of scenarios to overcome the ‘curse of dimensionality’. There is, however, an important requirement that is usually overlooked when one departs from the application domain of security pricing: the no-arbitrage condition. We formulate a moment matching model to generate multi-factor scenario trees for stochastic optimization satisfying no-arbitrage restrictions with a minimal number of scenarios and without any distributional assumptions. The resulting global optimization problem is quite general. However, it is non-convex and can grow significantly with the number of risk factors, and we develop convex lower bounding techniques for its solution exploiting the special structure of the problem. Applications to some standard problems from the literature show that this is a robust approach for tree generation. We use it to price a European basket option in complete and incomplete markets

Global method for a class of operation optimization problem in steel rolling systems

Many steel products are produced in hot or cold rolling lines with multiple stands. The steel material becomes thinner after being rolled at each stand. Steady-state parameters for controlling the rolling line need to be set so as to satisfy the final product specifications and minimize the total energy consumption. This paper develops a generalized geometric programming model for this setting problem and proposes a global method for solving it. The model can be expressed with a linear objective function and a set of constraints including nonconvex ones. Through constructing lower bounds of some components, the constraints can be converted to convex ones approximately. A sequential approximation method is proposed in a gradually reduced interval to improve accuracy and efficiency. However, the resulting convex programming model in each iteration is still complicated. To reduce the power, it is transformed into a second-order cone programming (SOCP) model and solved using alternating direction method of multipliers (ADMM). The effectiveness of the global method is tested using real data from a hot-rolling line with seven stands. The results demonstrate that the proposed global method solves the problem effectively and reduces the energy consumption

Design Optimization of a Speed Reducer Using Deterministic Techniques

The optimal design problem of minimizing the total weight of a speed reducer under constraints is a generalized geometric programming problem. Since the metaheuristic approaches cannot guarantee to find the global optimum of a generalized geometric programming problem, this paper applies an efficient deterministic approach to globally solve speed reducer design problems. The original problem is converted by variable transformations and piecewise linearization techniques. The reformulated problem is a convex mixed-integer nonlinear programming problem solvable to reach an approximate global solution within an acceptable error. Experiment results from solving a practical speed reducer design problem indicate that this study obtains a better solution comparing with the other existing methods

Topics in linear and nonlinear discrete optimization

This work contributes to modeling, theoretical, and practical aspects of structured Mathematical Programming problems. Many real-world applications have nonlinear characteristics and can be modeled as Mixed Integer Nonlinear Programming problems (MINLP). Modern global solvers have significant difficulty handling large-scale instances of them. Several convexification and underestimation techniques were proposed in the last decade as a part of the solution process, and we join this trend. The thesis has three major parts. The first part considers MINLP problems containing convex (in the sense of continuous relaxations) and posynomial terms (also called monomials), i.e. products of variables with some powers. Recently, a linear Mixed Integer Programming (MIP) approach was introduced for minimization the number of variables and transformations for convexification and underestimation of these structured problems. We provide polyhedral analysis together with separation for solving our variant of this minimization subproblem, containing binary and bounded continuous variables. Our novel mixed hyperedge method allows to outperform modern commercial MIP software, providing new families of facet-defining inequalities. As a byproduct, we introduce a new research area called mixed conflict hypergraphs. It merges mixed conflict graphs and 0-1 conflict hypergraphs. The second part applies our mixed hyperedge method to a linear subproblem of the same purpose for another class of structured MINLP problems. They contain signomial terms, i.e. posynomial terms of both positive and negative signs. We obtain new facet-defining inequalities in addition to those families from the first part. The final part is dedicated to managing guest flow in Georgia Aquarium after the Dolphin Tales opening with applying a large-scale MINLP. We consider arrival and departure processes related to scheduled shows and develop three stochastic models for them. If demand for the shows is high, all processes become interconnected and require a generalized model. We provide and solve a Signomial Programming problem with mixed variables for minimization resources to prevent and control congestions.Ph.D

Arbitrarily tight aBB underestimators of general non-linear functions over sub-optimal domains

In this paper we explore the construction of arbitrarily tight αBB relaxations of C2 general non-linear non-convex functions. We illustrate the theoretical challenges of building such relaxations by deriving conditions under which it is possible for an αBB underestimator to provide exact bounds. We subsequently propose a methodology to build αBB underestimators which may be arbitrarily tight (i.e., the maximum separation distance between the original function and its underestimator is arbitrarily close to 0) in some domains that do not include the global solution (defined in the text as “sub-optimal”), assuming exact eigenvalue calculations are possible. This is achieved using a transformation of the original function into a μ-subenergy function and the derivation of αBB underestimators for the new function. We prove that this transformation results in a number of desirable bounding properties in certain domains. These theoretical results are validated in computational test cases where approximations of the tightest possible μ-subenergy underestimators, derived using sampling, are compared to similarly derived approximations of the tightest possible classical αBB underestimators. Our tests show that μ-subenergy underestimators produce much tighter bounds, and succeed in fathoming nodes which are impossible to fathom using classical αBB

Modeling and Optimization of Gas Networks in Refinery

Master'sMASTER OF ENGINEERIN

RENEWABLE ENERGY MANAGEMENT FOR NON-DEFERRABLE LOADS WITH DYNAMIC ELECTRICITY PRICING

Ph.DDOCTOR OF PHILOSOPH

Analysis and Design of Communication Policies for Energy-Constrained Machine-Type Devices

This thesis focuses on the modelling, analysis and design of novel communication strategies for wireless machine-type communication (MTC) systems to realize the notion of Internet of things (IoT). We consider sensor based MTC devices which acquire physical information from the environment and transmit it to a base station (BS) while satisfying application specific quality-of-service (QoS) requirements. Due to the wireless and unattended operation, these MTC devices are mostly battery-operated and are severely energy-constrained. In addition, MTC systems require low-latency, perpetual operation, massive-access, etc. Motivated by these critical requirements, this thesis proposes optimal data communication policies for four different network scenarios. In the first two scenarios, each MTC device transmits data on a dedicated orthogonal channel and either (i) possess an initially fully charged battery of finite capacity, or (ii) possess the ability to harvest energy and store it in a battery of finite capacity. In the other two scenarios, all MTC devices share a single channel and are either (iii) allocated individual non-overlapping transmission times, or (iv) randomly transmit data on predefined time slots. The proposed novel techniques and insights gained from this thesis aim to better utilize the limited energy resources of machine-type devices in order to effectively serve the future wireless networks. Firstly, we consider a sensor based MTC device communicates with a BS, and devise optimal data compression and transmission policies with an objective to prolong the device-lifetime. We formulate joint optimization problems aiming to maximize the device-lifetime whilst satisfying the delay and bit-error-rate constraints. Our results show significant improvement in device-lifetime. Importantly, the gain is most profound in the low latency regime. Secondly, we consider a sensor based MTC device that is served by a hybrid BS which wirelessly transfers power to the device and receives data transmission from the device. The MTC device employs data compression in order to reduce the energy cost of data transmission. Thus, we propose to jointly optimize the harvesting-time, compression and transmission design, to minimize the energy cost of the system under given delay constraint. The proposed scheme reduces energy consumption up to 19% when data compression is employed. Thirdly, we consider multiple MTC devices transmit data to a BS following the time division multiple access (TDMA). Conventionally, the energy-efficiency performance in TDMA is optimized through multi-user scheduling, i.e., changing the transmission time allocated to different devices. In such a system, the sequence of devices for transmission, i.e., who transmits first and who transmits second, etc., does not have any impact on the energy-efficiency. We consider that data compression is performed before transmission. We jointly optimize both multi-user sequencing and scheduling along with the compression and transmission rate. Our results show that multi-user sequence optimization achieves up to 45% improvement in the energy-efficiency at MTC devices. Lastly, we consider contention resolution diversity slotted ALOHA (CRDSA) with transmit power diversity where each packet copy from a device is transmitted at a randomly selected power level. It results in inter-slot received power diversity, which is exploited by employing a signal-to-interference-plus-noise ratio based successive interference cancellation (SIC) receiver. We propose a message passing algorithm to model the SIC decoding and formulate an optimization problem to determine the optimal transmit power distribution subject to energy constraints. We show that the proposed strategy provides up to 88% system load performance improvement for massive-MTC systems

Essays on teamwork

Külpmann P. Essays on teamwork. Bielefeld: Universität Bielefeld; 2016

Optimal Risk-Based Design of Hydraulic Structures

National Science Foundation Research Initiation Grant ENG 78-5449Center for Water and the Environmen