Convex mixed-integer nonlinear programming
From DDWiki
Convex mixed-integer nonlinear programming refers to optimization problems of the form:
| minimize | 
|
| with respect to | 
|
| subject to | 
|
| |
| |
|
where and 
are convex functions of the vectors 
and 
, 
is an affine function of the vectors and , n and m are positive integers, and 
is the set of integers.
Contents |
Theory
Methods
Software
- DICOPT
- Author: Ignacio Grossmann at the Engineering Design Research Center (EDRC)at Carnegie Mellon University)
- Method: An outer approximation method for optimizing convex MINLPs by solving MILP (lower bound) and NLP (upper bound) sub-problems iteratively.
- Links:
- SBB
- Author: ARKI Consulting & Development
- Method: A branch and bound algorithm for solving convex MINLPs; lower bounds are obtained by solving the relaxed NLPs.
- Links:
- Comparison of DICOPT and SBB: DICOPT should perform better on models that have a signifficant and difficult combinatorial part, while SBB may perform better on models that have fewer discrete variables but more difficult nonlinearities (and possibly also on models that are fairly non convex).
- MINLPBB
- Author: Roger Fletcher, and Sven Leyffer
- Method: MINLP implements a branch and bound algorithm searching a tree whose nodes correspond to continuous nonlinearly constrained optimization problems. The continuous problems are solved using filterSQP.
- Links:
- MINOPT
- Author: Schweiger, Floudas
- Method: MINOPT is modeling language and algorithmic framework for the solution of LP, NLP, and convex MINLP problems; in particular, it has solvers for problems involving system of differential and algebric equations. for MINLPs, MINOPT employes: generalized Benders decomposition (GBD), outer approximation and Variants (OA, OA/ER, OA/ER/AP), generalized cross decomposition (GCD)
- Links:
