TTK4135 Optimization and control B.Foss Spring semester 2005

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TTK4135 Optimization and controlSpring semester
2005
Scope - this you shall learn Optimization -
important concepts and theory Formulating an
engineering problem into an optimization
problem Solving an optimization problem -
algorithms, coding and testing
Course information Lectures are given by
professor Bjarne A. Foss The course assistant is
Mr. K. Rambabu.
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Course information All course information is
provided on the web-pages for the course
www.itk.ntnu.no/fag/TTK4135. There will be no
hand-out of material. Every student must access
the course web-pages at least every week to keep
updated course information (eg. changes in
lecture times, information on mid-term exam) All
students should subscribe to the email-list
4135-optreg The deadlines for all assignments
(øvinger and the helicopter lab. report) are
absolute. There will be 1-2 øvingstimer with
assistants present ahead of the deadline for
every assignment. A minimum number of øvinger
and the helicopter lab.report must be approved to
enter the final examination. I will not cover the
complete curriculum in my lectures rather focus
on the most important and difficult parts.
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Grading The final exam counts 70 on the final
grade The mid-term exam is graded. It counts 15
on the final grade. Please note that only this
semesters mid-term exam counts. A mid-term grade
from last year will not be acknowledged. The
project report (based on the helicopter
laboratory) is graded. It counts 15 on the final
grade. Please note that only this semesters
report counts. A report grade from an earlier
year will not be acknowledged. To ensure
participation from all students 4 groups will be
selected for an oral presentation of their
laboratory work. This presentation will influence
the grade on the report.
Finally I welcome constructive criticism on all
aspects of the course, including my lectures.
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Preliminary lecture plan The content of each
lecture is specified in the following slides. All
lectures are given in lecture halls EL 3 and EL
6. The mid-term examination is on 2004-03-11. The
final examination is on 2004-05-23.
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Content of Lecture 1 - 2004-01-10 Optimization
problems appear everywhere Stock portfolio
management Resource allocation (airline
companies, transport companies, oil well
allocation problem) Optimal adjustment of a
PID-controller Formulating an optimization
problem From an engineering problem to a
mathematical description. Case a realistic
production planning problem Defining an
optimization problem Definition of important
terms Convexity and non-convexity Global vs.
local solution Constrained vs. unconstrained
problems Feasible region Reference Chapter 1 in
Nocedal and Wright (NW)
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Content of Lecture 2 - 2004-01-14 Karush
Kuhn-Tucker (KKT) conditions Sensitivities and
Lagrange-multipliers Reference Chapter 12.1,
12.2 in NW
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Content of Lecture 3 - 2004-01-17 Linear algebra
(App. A.2 in NW) Norms of vectors and
matrices Positive definit and indefinite
matrices Condition number, well-conditioned and
ill-conditioned linear equations Subspaces null
space and range space of a matrix Eigenvalue and
singular-value decomposition Matrix
factorization Cholesky factorization, LU
factorization Sequences (App.A.1, Ch.2.2 Rates
of in NW) Convergence to some points
convergence rate order notation Sets (App.A.1 in
NW) Open, closed, bounded sets Functions
(App.A.1 in NW) Continuity, Lipschitz
continuity Directional derivatives
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Content of Lecture 4 5 - 2004-01-21/28 Linear
programming - LP Mathematical formulation Conditio
n for optimality - the Karush-Kuhn-Tucker (KKT)
conditions Basic solutions - basis for the
Simplex method The Simplex method Understanding
the solution - Lagrange variables The dual
problem Obtaining an initial feasible
solution Efficiency of algorithms LP example -
production planning Reference Ch.12.2,13-13.5
in textbook
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Content of Lecture 6 - 2004-01-31 Quadratic
programming - QP Mathematical formulation Convex
vs. non-convex problems Condition for optimality
- KKT conditions Special case No inequality
conditions Reduced space methods The active-set
method for convex problems Understanding the
solution - Lagrange variables The dual
problem Obtaining an initial feasible
solution Efficiency of algorithms QP example -
production planning (varying sales
price) Reference Ch.12.2,16.1-16.4,(16.5),16.8
in textbook
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Content of Lecture 7 - 2004-02-04 Quadratic
programming - QP The active-set method for convex
problems The active-set method for non-convex
problems QP example - production planning
(varying sales price) Reference 16.4,16.5,16.8
in textbook
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Content of Lecture 8 - 2004-02-07 Quadratic
programming - QP The active-set method for
non-convex problems Reference 16.5,16.8 in
textbook
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Content of Lecture 9 - 2004-02-11 Repetition of
LP, QP --- Optimality conditions Necessary and
sufficient conditions for optimality Iterative
solution methods Starting point Search
direction Step length Termination
criteria Convergence Reference 2.1, 2.2 in
textbook
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Content of Lecture 10 - 2004-02-14 Line search
methods Choice of Wolfe-conditions Back-tracking
Curve-fit and interpolation Convergence of
line-search methods - Theorem 3.2 Convergence
rate Reference 3.1-3.4 in textbook
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Content of Lecture 11 - 2004-02-18 Practical
Newton-methods Approximate Newton-step Line
search Newton Modified Hessian Reference 6 - 6.3
in textbook Computing gradients Reference 7 -
7.1 in textbook
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Content of Lecture 12 - 2004-02-21 Quasi Newton
methods DFP and BFGS methods Rosenbrock example
for illustration Reference 8 - 8.1 in textbook
Information on the mid.term examination
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Content of Lecture 13 - 2004-03-07 Mid-term
examination
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Content of Lecture 14 - 2004-04-01 Mid-term
examination - once again Model Predictive Control
(MPC) The MPC principle Formulation of linear
MPC Formulating the optimisation problem which
is a QP-problem Reference Ch.1 and 2 Note on
MPC by M.Hovd
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Content of Lecture 15 - 2004-04-04 Linear
Quadratic Control (LQ-control) Formulation of the
LQ-problem Finite horizon LQ-control Reference
Ch.1-1.2 - Note on LQ-control by B.Foss
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Content of Lecture 16 - 2004-04-08 Linear
Quadratic Control (LQ-control) Infinite horizon
LQ-control State-estimation (repetition from
TTK4115) Reference Ch.1.3-1.4 - Note on
LQ-control by B.Foss
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Content of Lecture 17 - 2004-04-11 Model
Predictive Control (MPC) Feasibility and
constraint handling Target calculation Robustnes
s Reference Ch.4 6, 8, 9 Note on MPC by
M.Hovd
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Content of Lecture 18 - 2004-04-18 Nonlinear
programming - SQP Line-search in nonlinear
programming l1 exact merit function Exact merit
function Reference 15.3,18.5,18.6 in textbook
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Content of Lecture 19 - 2004-04-25 Nonlinear
programming - SQP Computing the search
direction Solving nonlinear equtions Quasi-Newton
method for computing the Hessian Reference
11.1,18.1-18.4,18.6 in textbook
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Content of Lecture 20 - 2004-05-02 Nonlinear
programming - SQP Reduced Hessian
methods Convergence rate Maratos
effect Reference 18.7,18.10,18.11 in textbook
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Content of Lecture 21 - 2004-05-09 SQP final
remarks including examples Repetition Repetition
of main topics Course evaluation -----------------
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