## Discrete Optimization

Start Date: 07/05/2020

 Course Type: Common Course

Explore 1600+ online courses from top universities. Join Coursera today to learn data science, programming, business strategy, and more. Tired of solving Sudokus by hand? This class teaches you how to solve complex search problems with discrete optimization concepts and algorithms, including constraint programming, local search, and mixed-integer programming. Optimization technology is ubiquitous in our society. It schedules planes and their crews, coordinates the production of steel, and organizes the transportation of iron ore from the mines to the ports. Optimization clears the day-ahead and real-time markets to deliver electricity to millions of people. It organizes kidney exchanges and cancer treatments and helps scientists understand the fundamental fabric of life, control complex chemical reactions, and design drugs that may benefit billions of individuals. This class is an introduction to discrete optimization and exposes students to some of the most fundamental concepts and algorithms in the field. It covers constraint programming, local search, and mixed-integer programming from their foundations to their applications for complex practical problems in areas such as scheduling, vehicle routing, supply-chain optimization, and resource allocation.

#### Course Syllabus

These lectures and readings give you an introduction to this course: its philosophy, organization, and load. They also tell you how the assignments are a significant part of the class. This week covers the common input/output organization of the assignments, how they are graded, and how to succeed in this class. #### Course Introduction

Discrete Optimization Optimization is the application of linear algebra to discrete problems. In particular, we deal with the problem of finding an optimal solution to a given problem. In contrast to classical problems, we consider discrete time and space constraints, which are inherent in all problems. An introduction to discrete optimization is given in the second module. We then delude ourselves into thinking that we are dealing with discrete problems by including in our programming the discrete optimization problem QORAC. We will see that there are efficient solutions to these problems. Next we consider the question of how to implement discrete optimization in a computer. We will see that the answer to this problem can be found using the classic programming style of recursion. The course also provides a basic introduction to the foundations of computer science. We will have a look at optimization in general, and also consider the multidimensional nature of computer problems.Introduction to Discrete Optimization Dynamic Programming Recursion Dynamic Programming with DMAIC & FUNCTION TRACKING Dominant Women: How to Survive the Power Struggle This course will examine the most fundamental challenges that women in management face today—by examining the individual choices women face, the conditions under which they face them, and the outcomes of those choices. We’ll look at these challenges from three different perspectives: the perspective of women in leadership, the perspective of people in

#### Course Tag

Constraint Programming Branch And Bound Discrete Optimization Linear Programming (LP)

#### Related Wiki Topic

Article Example
Discrete optimization Two notable branches of discrete optimization are:
Discrete optimization Discrete optimization is a branch of optimization in applied mathematics and computer science.
Discrete optimization As opposed to continuous optimization, some or all of the variables used in a discrete mathematical program are restricted to be discrete variables—that is, to assume only a discrete set of values, such as the integers.
Combinatorial optimization For NP-complete discrete optimization problems, current research literature includes the following topics:
Discrete optimization These branches are closely intertwined however since many combinatorial optimization problems can be modeled as integer programs (e.g. shortest path) and conversely, integer programs can often be given a combinatorial interpretation.
Nearest neighbour algorithm algorithm fails. Discrete Optimization 1 (2004), 121-127.
Nearest neighbour algorithm Combinatorial Problems, Discrete Optimization 3 (2006), 288-298.
Correlation clustering that the optimization of the correlation clustering functional is closely related to well known discrete optimization methods.
Iterated local search defining a modification of local search or hill climbing methods for solving discrete optimization problems.
Combinatorial optimization Some research literature considers discrete optimization to consist of integer programming together with combinatorial optimization (which in turn is composed of optimization problems dealing with graph structures) although all of these topics have closely intertwined research literature. It often involves determining the way to efficiently allocate resources used to find solutions to mathematical problems.
Naum Z. Shor He made significant contributions to nonlinear and stochastic programming, numerical techniques for non-smooth optimization, discrete optimization problems, matrix optimization, dual quadratic bounds in multi-extremal programming problems.
William O. Baker Award for Initiatives in Research For his development of deep and innovative algorithms to solve fundamental problems in network, information extraction, and discrete optimization.
Center for Operations Research and Econometrics The current operations research areas include modelling and finding solutions to industrial economics problems, discrete optimization, linear and nonlinear optimization, and the calculation of equilibria.
Rainer Burkard Rainer Ernst Burkard (born January 28, 1943, Graz, Austria ) is an Austrian mathematician. His research interests include discrete optimization, graph theory, applied discrete mathematics, and applied number theory.
Combinatorial optimization There is a large amount of literature on polynomial-time algorithms for certain special classes of discrete optimization, a considerable amount of it unified by the theory of linear programming. Some examples of combinatorial optimization problems that fall into this framework are shortest paths and shortest path trees, flows and circulations, spanning trees, matching, and matroid problems.
Continuous optimization As opposed to discrete optimization, the variables used in the objective function are required to be continuous variables—that is, to be chosen from a set of real values between which there are no gaps (values from intervals of the real line). Because of this continuity assumption, continuous optimization allows the use of calculus techniques.
Combinatorial optimization Combinatorial optimization problems can be viewed as searching for the best element of some set of discrete items; therefore, in principle, any sort of search algorithm or metaheuristic can be used to solve them. However, generic search algorithms are not guaranteed to find an optimal solution, nor are they guaranteed to run quickly (in polynomial time). Since some discrete optimization problems are NP-complete, such as the traveling salesman problem, this is expected unless P=NP.
Peter L. Hammer Hammer founded the Rutgers University Center for Operations Research, and created and edited the journals "Discrete Mathematics", "Discrete Applied Mathematics", "Discrete Optimization", "Annals of Discrete Mathematics", "Annals of Operations Research", and "SIAM Monographs on Discrete Mathematics and Applications".
Correlation clustering Several discrete optimization algorithms are proposed in this work that scales gracefully with the number of elements (experiments show results with more than 100,000 variables).
Jon Lee (mathematician) Jon Lee (born 1960) is an American mathematician and operations researcher, the G. Lawton and Louise G. Johnson Professor of Engineering at the University of Michigan. He is known for his research in nonlinear discrete optimization and combinatorial optimization.