Tutorial Program Recent Developments of Optimization in Process Systems Engineering Wednesday 17 January 09.30–10.10 Registration with coffee & sandwich 10.10–10.15 Opening words 10.15–11.55 Modeling in Process Control and Systems Engineering from a Sparse Perspective Hannu Toivonen and Mikael Manngård, Åbo Akademi 12.00–13.00 Lunch 13.10–14.10 Optimization in Process Systems Engineering Jan Kronqvist, Åbo Akademi 14.15–15.15 Semidefinite Programming — Basics Ray Pörn, Åbo Akademi 15.15–15.30 Coffee break 15.30–17.00 Semidefinite Programming — Advanced Topics and Applications Ray Pörn, Åbo Akademi 19.00– Dinner You are encouraged to bring your own laptop to the tutorial with programs and toolboxes installed as explained in the topic outlines. NPCW Tutorial, 17 January 2018, Åbo, Finland 1
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Tutorial Program Recent Developments of Optimization in Process Systems Engineering
Wednesday 17 January
09.30–10.10 Registration with coffee & sandwich
10.10–10.15 Opening words
10.15–11.55 Modeling in Process Control and Systems Engineering from a Sparse Perspective Hannu Toivonen and Mikael Manngård, Åbo Akademi
12.00–13.00 Lunch
13.10–14.10 Optimization in Process Systems Engineering Jan Kronqvist, Åbo Akademi
14.15–15.15 Semidefinite Programming — Basics Ray Pörn, Åbo Akademi
15.15–15.30 Coffee break
15.30–17.00 Semidefinite Programming — Advanced Topics and Applications Ray Pörn, Åbo Akademi
19.00– Dinner
You are encouraged to bring your own laptop to the tutorial with programs and toolboxes installed as explained in the topic outlines.
NPCW Tutorial, 17 January 2018, Åbo, Finland 1
Sparse modeling in process control and process systems engineering
Hannu Toivonen and Mikael Manngård
Developments in sparse optimization during the last twenty years have made it possible to address
certain combinatorial optimization problems, which were previously deemed intractable. The
purpose of this tutorial is to describe some applications of sparse optimization in process control and
systems engineering. These include variable selection for predictive models, identification of
switching systems, system identification in the presence of trends, and identification of low-order
dynamic models.
The structure of the presentation is as follows:
1) Background: examples of combinatorial optimization problems
- Variable selection, i.e., finding a small subset from a given set of variables which explains
data. For example, for predictive models, or to explain fault situations.
- Change detection in data or model. For example: identification of switching systems, which
switch between a number of modes at unknown time instants, or estimation of piecewise
linear trends in data.
2) A basic problem: selection of independent variables in regression model
Here we describe how a combinatorial problem can be solved, either exactly or approximately,
by relaxing it to a convex l1-constrained problem. The most important properties of this
approach are reviewed.
3) System identification in the presence of trends and level shifts
Here we identify a system model and structured disturbances (such as trends, outliers and level
shifts) simultaneously using sparse optimization. Results are demonstrated on numerical
examples.
4) Identification of low-order system models
System order can be characterized in terms of the rank of a Hankel matrix associated with the
system’s impulse response. Identification of a low-order model can therefore be formulated as a
rank-constrained optimization problem. These are numerically hard problems, but can be
relaxed by replacing the matrix rank by its nuclear norm, defined as the sum of the matrix
singular values. The nuclear norm relaxation results in a convex optimization problem, for which
efficient solvers exist.
For the numerical examples in the tutorial the cvx toolbox in Matlab will be used.
NPCW Tutorial, 17 January 2018, Åbo, Finland 2
Optimization in process systems engineering
Jan Kronqvist
In this workshop we present some important types of optimization problems, with focus on how to solve these problems. We present some basic theory, methods and some problem formulations. We demonstrate how these problems can be solved efficiently in Matlab by the state-of-the-art solvers Gurobi and IPOPT.
1) A brief introduction to optimization
2) Integer programmingWe present techniques for solving linear problems containing integer variables, mainly thebranch and bound method and some cutting planes.
3) Disjunctive programmingHow to incorporate logic decisions in optimizations problems.
4) Solving optimization problems in MatlabWe show how to solve linear problems with integer variables in Matlab using Gurobi. We alsogive a brief illustration on how to use the nonlinear solver IPOPT with Matlab.
5) Optimization problems with nonlinear functionsHow can we solve optimization problems with both nonlinear functions and integer variables?
In this workshop we will use the solvers Gurobi and IPOPT in Matlab. There are free Academic licenses available for both solvers and we encourage participant to obtain these in advance.
Opti toolbox which contains IPOPT and some other powerful solvers can be obtained from: https://www.inverseproblem.co.nz/OPTI/
Gurobi which is one of the most powerful solvers for linear and quadratic optimization problems can be obtained directly from: http://www.gurobi.com/ There is an interface to Matlab which is easy to set up. Obtaining the Academic license takes less than 5 minutes (can only be done with a university network connection).