Convex¶

bilinear problem¶

• x * y

• e^x y + y

• sin(x + y) - x^2

  obj: x * y
  var: x, y
  

McCormick envelopes¶

The McCormick Envelope is a type of convex relaxation used for the optimization of bilinear non-linear programming (NLP) problems: https://optimization.cbe.cornell.edu/index.php?title=McCormick_envelopes

Convex-Concave Procedure (CCP)¶

If objective is not convex but can be expressed as f_convex - g_convex:

• Use first order Taylor approximation to replace g_convex

• So objective will become convex

• Run multiple iterations to converge to local minimum

• No guarantee for global minimum (maybe a big issue for some problems)