Successive linear programming (SLP) model for a financial planning problem
Description
- modifying constraint coefficients
- while statement
- basis in- and output and problem reloading
- setting/accessing optimiser parameters
- procedure
Further explanation of this example:
'Mosel User Guide', Section 12.1 Recursion
Source Files
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fin_nl.mos
(!******************************************************
Mosel User Guide Example Problems
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file fin_nl.mos
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Financial application solved by SLP.
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, June 2003, rev. Jul. 2023
*******************************************************!)
model "Recursion (NLP)"
uses "mmxnlp" ! Use Xpress NonLinear
declarations
NT=6 ! Time horizon
QUARTERS=1..NT ! Range of time periods
M,P,V: array(QUARTERS) of real ! Payments
interest: array(QUARTERS) of mpvar ! Interest
net: array(QUARTERS) of mpvar ! Net
balance: array(QUARTERS) of mpvar ! Balance
rate: mpvar ! Interest rate
end-declarations
M:: [-1000, 0, 0, 0, 0, 0]
P:: [206.6, 206.6, 206.6, 206.6, 206.6, 0]
V:: [-2.95, 0, 0, 0, 0, 0]
setinitval(rate, 0) ! Set initial values for variables
forall(t in QUARTERS) setinitval(balance(t), 1)
! net = payments - interest
forall(t in QUARTERS) net(t) = (M(t)+P(t)+V(t)) - interest(t)
! Money balance across periods
forall(t in QUARTERS) balance(t) = if(t>1, balance(t-1), 0) - net(t)
! Interest rate
forall(t in 2..NT) -(365/92)*interest(t) + balance(t-1) * rate = 0
interest(1) = 0 ! Initial interest is zero
forall (t in QUARTERS) net(t) is_free
forall (t in 1..NT-1) balance(t) is_free
balance(NT) = 0 ! Final balance is zero
! setparam("XNLP_VERBOSE",true) ! Uncomment to see detailed output
setparam("XPRS_NLPSOLVER", 1) ! Use a local NLP solver
setparam("XNLP_SOLVER", 0) ! Select the SLP solver
minimize(0) ! Solve the problem (get feasible)
! Print the solution
writeln("\nThe interest rate is ", getsol(rate))
write(strfmt("t",5), strfmt(" ",4))
forall(t in QUARTERS) write(strfmt(t,5), strfmt(" ",3))
write("\nBalances ")
forall(t in QUARTERS) write(strfmt(getsol(balance(t)),8,2))
write("\nInterest ")
forall(t in QUARTERS) write(strfmt(getsol(interest(t)),8,2))
writeln
end-model
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