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Current industrial practice knows many optimization tasks that can be cast as mixed-integer optimal control problems. Due to the combinatorial character of these problems, the computation of optimal solutions under real-time constraints is still a demanding challenge.
Starting with Bock's direct multiple shooting method for optimal control, Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates can be given even after discretization and rounding. In a sequential quadratic programming framework, extensive exploitation of arising structures in an active set method ultimately brings the developed algorithm towards real-time feasibility.
Inhaltsverzeichnis
From The Contents:
- The Direct Multiple Shooting Method for Optimal Control
- Mixed-Integer Optimal Control
- Constrained Nonlinear Programming
- Mixed-Integer Real-Time Iterations
- Outer Convexification of Constraints
- A Nonconvex Parametric SQP Method
- Linear Algebra for Block Structured QPs
- Updates for the Block Structured Factorization
Über den Autor / die Autorin
Dr. Christian Kirches is a postdoctoral researcher in the simulation and optimization group at the chair of Professor Dr. Dr. h.c. Hans Georg Bock at the Interdisciplinary Center for Scientific Computing (IWR) of Heidelberg University.
Zusammenfassung
Current industrial practice knows many optimization tasks that can be cast as mixed-integer optimal control problems. Due to the combinatorial character of these problems, the computation of optimal solutions under real-time constraints is still a demanding challenge.
Starting with Bock's direct multiple shooting method for optimal control, Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates can be given even after discretization and rounding. In a sequential quadratic programming framework, extensive exploitation of arising structures in an active set method ultimately brings the developed algorithm towards real-time feasibility.
Zusatztext
From the book reviews:
“The book under review gives a useful introduction and presents valuable new contributions in this topic. … The material is very clearly written and certain parts … may well support graduate education. The targeted audience of the book is applied mathematicians and engineers.” (Gábor Szederkényi, Mathematical Reviews, January, 2015)
Bericht
From the book reviews:
"The book under review gives a useful introduction and presents valuable new contributions in this topic. ... The material is very clearly written and certain parts ... may well support graduate education. The targeted audience of the book is applied mathematicians and engineers." (Gábor Szederkényi, Mathematical Reviews, January, 2015)
