Igor Griva

NONLINEAR OPTIMIZATION AND APPLICATIONS

The course focuses on theoretocal and practical aspects of nonlinear optimization. One of the goal of this class is to show students how to use modern optimization tools in order to solve important problems arising in many areas of science and engineering. We consider problems in the following areas: data analysis, computational learning, mechanics, optical design, trajectory optimization, shape optimization, optimal control and finance. The course demonstrates that many real world problems can be modeled as optimization problems and solved by widely available optimization tools. Throughout the course we present various optimization models and demonstrate how to solve them using optimization software. These models are expressed in the AMPL modeling language. This language is used as a common mechanism for conveying optimization problems. The course emphasizes the importance of proper modeling. One of the main point this course illustrates is that often a real world problem can have multiple equivalent mathematical formulations some of which are numerically tractable while others are not. Basics of nonlinear optimization theory will be also discussed.

• Schedule: M 7:20-10:00 pm, Exploratory Hall 4106
• Office Hours: M 10:00 - 11:00 pm, Exploratory Hall, Rm 4114
• Fall 2022

The Department of Mathematical Sciences

Department of Mathematical Sciences
4400 University Drive, MS: 3F2
Exploratory Hall, room 4400
Fairfax, Virginia 22030
Phone Number: 703-993-1460
Fax Number: 703-993-1491

The Center for Simulation and Modelling

Researchers in the Computational Materials Science Center focus on the discovery, interpretation, simulation, and organization of the microscopic interactions between atoms and molecules in condensed phases of materials including biomaterials. The ability to predict materials properties is a fundamental requirement of technological advances and economic competitiveness.

Linear and Nonlinear Optimization

This book introduces the applications, theory, and algorithms of linear and nonlinear optimization, with an emphasis on the practical aspects of the material. Its unique modular structure provides flexibility to accommodate the varying needs of instructors, students, and practitioners with different levels of sophistication in these topics. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support vector machines.

• Coursebook for Graduate Students
• Publisher: SIAM
• Year: 2008