Xpress Nonlinear examples
Examples of using Xpress Nonlinear through the Mosel module mmxnlp.
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| Locate airport while minimizing average distance: quadratic constraints and objective
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| Type: |
QCQP |
| Rating: |
1 (simple) |
| Description: |
Locate N airports each within a specified distance of a city centre, and minimise
the sum of square of the distances between all the airports.
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| File(s): |
airport_nl.mos, airport_nl_graph.mos |
| Data file(s): |
airport.dat |
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| Maximise discount at a bookstore: Discrete variables
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| Type: |
discrete NLP |
| Rating: |
2 (easy-medium) |
| Description: |
A bookstore has the following discount policy:
For each $1 you spend you get 0.1% discount on your next purchase.
Example: If you have to buy three books that cost $10, $20 and $30, you could buy the $30 book today,
the $10 book tomorrow (on which you'll get a 3% discount), and the $20 book the following day
(on which you'll get a 1% discount). Or you could buy the $30 book and the $20 book today,
and the $10 book tomorrow (with a 5% discount).
What is the cheapest way to buy N books (for given prices) ?
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| File(s): |
bookdisc.mos |
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| Nonlinear objective with integer decision variables: Discrete variables
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| Type: |
discrete NLP |
| Rating: |
2 (easy-medium) |
| Description: |
The examples describe problems with a nonlinear objective function and some integer
decision variables.
- A craftsman wants to optimise its revenue based on the size of the produced
wooden boxes (boxes02.mos)
- Dealers sell apples at a market at the same price and the game is to find
the quantity sold and the associated price (pricechange.mos).
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| File(s): |
boxes02.mos, pricechange.mos, pricechange_graph.mos |
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| Determine chain shape: Quadratic constraints
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| Type: |
QCQP |
| Rating: |
2 (easy-medium) |
| Description: |
Find the shape of a hanging chain by minimising its potential energy.
The problem is formulated as a QCQP problem (linear objective, convex quadratic constraints).
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| File(s): |
catenary.mos, catenary_graph.mos |
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| Facility location: Nonlinear objective
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| Type: |
Convex NLP |
| Rating: |
2 (easy-medium) |
| Description: |
Euclidean facility location problem. |
| File(s): |
emfl.mos, emfl_graph.mos |
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| Approximation of a function: Approximation of a function
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| Maximal inscribing square: Trigonometric functions
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| Type: |
Nonconvex NLP |
| Rating: |
3 (intermediate) |
| Description: |
Computing a maximal inscribing square for the curve
(sin(t)*cos(t), sin(t)*t). Comparison of results with different solver choices.
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| File(s): |
inscribedsquare.mos, inscribedsquare_graph.mos |
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| Static load balancing in a computer network: Nonlinear objective
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| Type: |
Convex NLP |
| Rating: |
2 (easy-medium) |
| Description: |
Static load balancing in a tree computer network with two-way traffic.
A set of heterogeneous host computers are interconnected; every
node processes jobs (the jobs arrive at each node according to a time
invariant Poisson process) locally or sends it to a remote node.
In the latter case, there is a communication delay for forwarding the job
and getting a response back.
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| File(s): |
loadbal.mos, loadbal_graph.mos |
| Data file(s): |
loadbal.dat |
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| Minimum surface between boundaries: Nonlinear constraints and objective
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| Type: |
Convex NLP |
| Rating: |
2 (easy-medium) |
| Description: |
Minimizing the surface between given boundaries with an optional obstacle. |
| File(s): |
minsurf.mos, minsurf_graph.mos |
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| Moon landing: Nonlinear objective and constraints
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| Type: |
Nonconvex NLP |
| Rating: |
3 (intermediate) |
| Description: |
A rocket is fired from the earth and must land on a particular location on the moon.
The goal is to minimize the total consumed fuel.
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| File(s): |
moonshot.mos, moonshot_graph.mos |
| Data file(s): |
moonshot.dat |
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| Polygon construction under constraints: Trigonometric constraints and objective
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| Type: |
NLP |
| Rating: |
3 (intermediate) |
| Description: |
The set of examples describe models to create a polygon with various constraints and goals:
- Polygon is formulated by algebraic expressions (polygon1.mos)
- Polygon is formulated by a user function (polygon2.mos)
- Polygon is formulated by a user procedure (polygon3.mos)
- Polygon is defined by a function present in Java (polygon8.mos, Polygon.java)
- Polygon is defined by a function present in Java returning its own derivatives (polygon8_delta.mos, Polygon.java)
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| File(s): |
polygon1.mos, polygon1_graph.mos, polygon2.mos, polygon3.mos, polygon8.mos, polygon8_delta.mos |
| Data file(s): |
Polygon.java |
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| Portfolio optimization: Quadratic constraints and quadratic objective
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| Type: |
QCQP |
| Rating: |
2 (easy-medium) |
| Description: |
The example describes a portfolio optimization problem with parameterized risk/return measures.
It is formulated with quadratic constraints and a quadratic objective function.
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| File(s): |
portfoliorisk.mos, portfoliorisk_graph.mos |
| Data file(s): |
portfoliorisk.dat |
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| Locating electrons on a conducting sphere: Nonlinear constraint and objective, alternative objective functions
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| Type: |
Nonconvex NLP |
| Rating: |
3 (intermediate) |
| Description: |
Finds the equilibrium state distribution of electrons positioned on a conducting sphere.
The problem is formulated as a nonconvex NLP problem.
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| File(s): |
sphere.mos, sphere_graph.mos |
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| Find the shape of a chain of springs: Quadratic constraints
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| Type: |
SOCP |
| Rating: |
2 (easy-medium) |
| Description: |
Find the shape of a hanging chain where each chain link is a spring. |
| File(s): |
springs.mos, springs_graph.mos |
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| Steiner tree problem: Quadratic constraints
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| Trafic equilibrium: Nonlinear objective
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| Modeling hang glider trajectory: Nonlinear constraints, trapezoidal discretization
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| Type: |
NLP |
| Rating: |
4 (medium-difficult) |
| Description: |
Maximize the total horizontal distance a hang glider flies subject to different configurable wind conditions. |
| File(s): |
glidert.mos, glidert_graph.mos |
| Data file(s): |
glider.dat |
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| Force required to lift an object: SOCP formulation
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| Type: |
SOCP |
| Rating: |
3 (intermediate) |
| Description: |
Find the smallest amount of force required to lift an object, grasping it at a set of possible grasping points. |
| File(s): |
grasp.mos, grasp_graph.mos |
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| Maximize the sum of radii of N non-overlapping circles in a square: Nonlinear constraints, Nonconvex-QCP, circle packing
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| Type: |
NLP |
| Rating: |
3 (intermediate) |
| Description: |
Maximize the sum of the radius of N non-overlapping circles inside the unit square. |
| File(s): |
circlepacking.mos |
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| Minimize the pairwise distance ratio for N points: Nonlinear constraints, Nonconvex-QCP, squared distance, ratio
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| Type: |
NLP |
| Rating: |
3 (intermediate) |
| Description: |
Determine positions for N points in a D-dimensional space such that the ratio of the maximum to minimum squared pairwise distances is minimized. This promotes a uniform distribution of points, minimizing clustering and maximizing spatial efficiency.
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| File(s): |
pairwisedistance.mos |
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