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**Authors:** H. Y. Benson, Vanderbei

**Version:** 5.04, 8/2000;

**Available:** yes, from http://orfe.princeton.edu/ loqo/

**Key paper:** [27]

**Features:** NLP approach

**Language, Input format:** C; SDPA, Matlab, AMPL

**Error computations:** no

**Solves:** SOCP (SDP)
LOQO is a software package for solving general (smooth) nonlinear optimization problems of the form

where
,
,
is the set of
equalities,
is the set of inequalities,
, and
.
It implements an infeasible-primal-dual
path-following method and requires that the problem be smooth, that is and
be twice differentiable, and be an affine function.
Even though LOQO can handle nonconvex problems in general, it performs
better with convex problems, where is convex, are affine,
and are concave functions.
Stopping criteria

- LOQO can handle other types of nonlinear constraints in the problem.
- A weakness results from the use of the Cholesky factorization. LOQO
works best with a sparse problem, and it does not exploit the special
structure of an SOCP.
- Its SDP approach leads to dense problems.

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Hans D. Mittelmann
2002-08-17