# How to turn a dot into simple scaler expressions for nonlinear optimization using JUMP

I want to turn the dot notation in this code to simple scaler operations for NLconstraint.
I’ve checked the examples in JUMP’s documentation, but I could not get it to work.
The following is the part that’s causing the issue.

``````    @NLobjective(model, Min,
100 * sum(position[:, end].^2)+ sum(velocity[:, end].^2))

# Initial conditions:
@NLconstraint(model, position[:, 1] .== initial_position)
@NLconstraint(model, velocity[:, 1] .== initial_velocity)
@NLconstraint(model, angle[1] .== initial_angle)

optimize!(model)
return value.(position), value.(velocity), value.(acceleration), value.(angle)
``````

Here’s the entire optimizer function.

``````function run_mpc(initial_position, initial_velocity, initial_angle)

model = Model(Ipopt.Optimizer)

Δt = 0.1
num_time_steps = 20 # Change this -> Affects Optimization
max_acceleration_Thr = 10 # Max Thrust / Mass
max_pitch_angle = 90
accel_g = 1.635 # 1/6 of Earth G

@variables model begin
position[1:2, 1:num_time_steps]
velocity[1:2, 1:num_time_steps]
acceleration[1:2, 1:num_time_steps]
-max_pitch_angle <= angle[1:num_time_steps] <= max_pitch_angle
-max_acceleration_Thr <= accel_Thr[1:num_time_steps] <= max_acceleration_Thr
end

# Dynamics constraints
@NLconstraint(model, [i=2:num_time_steps, j=[1]], acceleration[j, i] == accel_Thr[i-1]*sind(angle[i-1]))

@NLconstraint(model, [i=2:num_time_steps, j=[2]], acceleration[j, i] == accel_Thr[i-1]*cos(angle[i-1])-accel_g)

@NLconstraint(model, [i=2:num_time_steps, j=1:2],
velocity[j, i] == velocity[j, i - 1] + (acceleration[j, i - 1]) * Δt)
@NLconstraint(model, [i=2:num_time_steps, j=1:2],
position[j, i] == position[j, i - 1] + velocity[j, i - 1] * Δt)

# Cost function: minimize final position and final velocity
# For Moving to [-2,0] with min. vertical velocity,
# sum(([-2,0]-position[:, end]).^2)+ sum(velocity[[2], end].^2)
@NLobjective(model, Min,
100 * sum(position[:, end].^2)+ sum(velocity[:, end].^2))

# Initial conditions:
@NLconstraint(model, position[:, 1] .== initial_position)
@NLconstraint(model, velocity[:, 1] .== initial_velocity)
@NLconstraint(model, angle[1] .== initial_angle)

optimize!(model)
return value.(position), value.(velocity), value.(acceleration), value.(angle)
end;
``````

If the constraint is linear or quadratic, you can use `@constraint`. That should work for these cases.

Otherwise you need an explicit sum like `sum(position[i, num_time_steps] for i in 1:2)`.

For the last part, use a collection

``````@constraint(model, [i=1:2], position[i, 1] == initial_position[i])
``````