MultiConvex

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Example 1

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@mcvx begin
  x = var()
  minimize((x - 1)^2)
end

result: x = 1.0

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Example 2

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u = randn(100)

@mcvx begin
  x = var(100);
  minimize(sum((x*x' - u*u').^2))
  init_randn()
  solver_newton(1000)
end

result: x = u

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function/type reference

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abstract MCExpr type of expressions supports operations: show +, -, *

function mcvx_begin() initializes an mcvx model

function var() function var(dim1::Int64) function var(dim1::Int64, dim2::Int64) produces a new variable in an mcvx scope, or an array of such variables

function minimize(expr::MCExpr) function maximize(expr::MCExpr) provides an objective for the problem

function solver_coorddesc(numiters::Int64, step_size::Float64) selects the first-order coordinate descent solver (default)

function solver_newton(numiters::Int64) function solver_newton(numiters::Int64, alpha::Float64) selects the second-order (newton's method) coordinate descent solver

function init_zero() specifies to initialize the problem variable to zero

function init_randn() specifies to initialize the problem variable with randn

function mcvx_end() finishes the mcvx model and solves the problem

function resolve(expr::MCExpr) after mcvx_end called, returns the value of a variable in the solution

macro var(symbol, dims...) wrapper around the var(...) function that gives the variable a name in the displayed version of the expression

macro mcvx(block) automatically wraps the block in appropriate mcvx_begin() and mcvx_end() statements, and automatically generates resolve(...) calls at the end to places the variables back into local scope