LFPSQP.jl

Julia implementation of Locally Feasibly Projected Sequential Quadratic Programming

Performs feasible nonlinear constrained optimization (i.e., every iterate satisfies the proposed constraints) on problems of the form:

where f is the objective function, c are equality constraints, d are inequality constraints with lower and upper bounds of d^l and d^u, and x^l and x^u are box constraints.

Please cite as:
K.S. Silmore and J.W. Swan, Locally Feasibly Projected Sequential Quadratic Programming for Nonlinear Programming on Arbitrary Smooth Constraint Manifolds, ArXiv:2111.03236 [math.OC] (2021).

Examples

Unconstrained

Let's optimize the classic Rosenbrock function:

f = x -> (1 - x[1])^2 + 100*(x[2] - x[1]^2)^2

x0 = [0.0, 0.0]

x, obj_values, λ_kkt, term_info = optimize(f, x0)

Here, x is the final value of the variables, obj_values is a vector of objective function values at each iterate (including the initial one), λ_kkt is a vector of Lagrange multipliers (here an empty vector), and term_info is a struct that summarizes the optimization procedure. For example,

term_info

produces

TerminationInfo:
condition = f_tol
       Δf = 1.0898882046786806e-7
   ||Δx|| = 0.0007384068067118611
||P(∇f)|| = 4.332627751789361e-5
    iters = 17

where condition is the termination criterion (here the change in objective function value was smaller than the default tolerance), Δf is the change in objective function value at the last iteration, ||Δx|| is the 2-norm of increment of the variables at the last iteration, ||P(∇f)|| is the 2-norm of the final objective function gradient, and iters is the total number of (outer) iterations taken.

Equality constrained

n = 50     # number of variables
m = 1      # number of constraints

f = x -> dot(x, x)

function c!(cval, x)
    cval[1] = x[1] - 0.75
end

x0 = ones(n)

x, obj_values, λ_kkt, term_info = optimize(f, c!, x0, m)

Inequality constrained

n = 50     # number of variables
m = 0      # number of equality constraints
p = 1      # number of inequality constraints

coeff = randn(n)
f = x -> dot(coeff, x)

# circle constraint
function d!(dval, x)
    dval[1] = dot(x, x) - 1.0
end

x0 = zeros(n)

xl = -Inf .* ones(n)       # no bound constraints
xu = Inf .* ones(n)

x, obj_values, λ_kkt, term_info = optimize(f, nothing, d!, x0, xl, xu, m, p)

To-do

Documentation
Handling of sparsity in constraints
Other miscellaneous features

richardrl / LFPSQP.jl