Online decision making under uncertainty and time constraints represents one of the most challenging problems for robust intelligent agents. This course will discuss both mathematical programming and heuristic approaches to solving combinatorial optimization problems. This course will address both optimal and heuristic approaches - cutting plane, branch-and-bound, branch-and-cut, Lagrangian relaxation, local search, simulated annealing, tabu search, genetic algorithms, and neural networks - to solving combinatorial optimization problems such as production planning and scheduling, operational management of distribution systems, timetabling, location and layout of facilities, routing and scheduling of vehicles and crews, etc.
Ability to formulate a wide range of management problems that can be solved to optimality by classical combinatorial optimization techniques and the knowledge of alternative solution approaches such as metaheuristics that can find nearly optimal solutions. The solution of optimal decision-making and engineering design problems in which the objective and constraints are nonlinear functions of potentially (very) many variables is required on an everyday basis in the commercial and academic worlds. Understanding the construction and main solution ideas for nonlinear optimization problems.
The detailed modelling of real life problems requires a knowledgeable choice of the objective function and constraints, and often leads to very large optimization problems. Data Science provides numerous instances of problems which can be modelled using optimization.
This course will address the methods for constrained optimization and the assumption will be made that the knowledge of an exact (or an approximation of) the second order information (Hessian of the Lagrangian) is available.
The successful applications of these techniques in various Data Science problems from areas such as statistics, machine learning, engineering, energy and finance, will be discussed. The practical component of this course will consist of computing laboratory work using Matlab (including the Matlab-based CVX system for convex optimization).
The course covers modern optimization algorithms and theory developed in recent years, suitable for big data applications; that is applications with millions or billions of design parameters and data points.

Problems of these sizes are ever more common as we live in a digital age in which it is increasingly easier to collect and store data in digital form (e.g.
New methods and tools are needed to analyze such vast datasets and optimization algorithms are at the heart of such efforts, underpinning much of data science, including machine learning, operations research and statistical analysis. The material is designed for students wishing to continue with PhD studies or those wishing to enter big data industry and is suitable for MSc students in quantitative disciplines (e.g. Applications of the methods covered in the course can be found virtually in all fields of data science including text analysis, page ranking, speech recognition, image classification, finance and decision sciences.
Munich (joinlty with CO), May 2014; Catania, May 2015 and Budapest is scheduled for May 2016. In an increasingly dynamic, interconnected, and real-time world, intelligent systems must adapt dynamically to uncertainties, update existing plans to accommodate new requests and events, and produce high-quality decisions under severe time constraints.
Awareness how difficult some practical optimization problems can be and the complex role performed by managers.
A closely-related subject is the solution of nonlinear systems of equations, also referred to as least-squares or data fitting problems that occur in almost every instance where observations or measurements are available for modelling a continuous process or phenomenon, such as in weather forecasting. First- and second-order optimality conditions for constrained optimization problems; overview of methods for constrained problems (active-set methods, sequential quadratic programming, interior point methods, penalty methods, filter methods). Ability to assess the quality of available methods and solutions for such problems, as well as to potentially develop such optimization techniques and implementations.
The efficient solution of such problems is a key to the success of optimization in practice.
The amount of data in some of these models challenges existing optimization techniques and requires the development of new ones.

The course will cover interior point methods for various classes of optimization problems, addressing their theory and implementation. These exercises will reinforce the theoretical analysis of problems, methods and their implementation.
Optimization is one of three pillars of big data analysis, with the other two being computer science and statistics. The mathematical analysis of such problems and study of the classical methods for their solution are fundamental for understanding both practical methods of solution and the nature of the solution which may be obtained.
The applications considered are: portfolio analysis, strategic planning, sequential sampling and production problems. This book presents a novel framework, online stochastic optimization, to address this challenge.This framework assumes that the distribution of future requests, or an approximation thereof, is available for sampling, as is the case in many applications that make either historical data or predictive models available.
Thus it imparts knowledge and insight into the optimal choice of available methods (software) or ability to develop such techniques for the practical problems at hand.
It assumes additionally that the distribution of future requests is independent of current decisions, which is also the case in a variety of applications and holds significant computational advantages.
The book presents several online stochastic algorithms implementing the framework, provides performance guarantees, and demonstrates a variety of applications. It discusses how to relax some of the assumptions in using historical sampling and machine learning and analyzes different underlying algorithmic problems.

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