[SCIP] No branching on solving NLP (number of nodes remains eq. to 1)

[Vladimir V. Voloshinov]

Dear SCIP developers,
we tried to solve some "middle-size" nonlinear problem with polynomial
functions in constraints with out any discrete variables (extr. from
NL-file header below)
 430 442 1 0 401 # vars, constraints, objectives, ranges, eqns
 199 1 0 0 0 0      # nonlinear constrs, objs; ccons: lin, nonlin, nd, nzlb
 129 221 26         # nonlinear vars in constraints, objectives, both
  0 0 0 0 0             # discrete variables: binary, integer, nonlinear
(b,c,o)
Some of nonlinear constraints are non-convex quadratic and others (100
totally) are 3rd order polynomial, i.e. sums of the items like "
<var1>*sqr(<var2>)"  (in CIP format).
Local solver IPOPT founds local optimum (we suspect that it is global) in
10 seconds.
But SCIP with default settings (and FiberSCIP) can not prove global
optimality in an hours and I DO NOT SEE ANY BRANCHING (domain
decomposition), see fragment of SCIP-log:
=============================
 time | node  | left  |LP iter    |LP it/n| mem |mdpt |frac |vars |cons
|cols |rows |cuts   | ,,, | dualbound       | primalbound  |  gap
 5004s|     1 |     0   | 12932k|     -      |  77M|   0     |   0  | 427 |
438 | 427 |  89k | 190k | ... |-2.167723e-01 | 1.615240e-01 |    Inf
...........
  358m|     1 |     0   | 31028k|     -     | 103M|   0    |   0   | 427 |
438 | 427 | 126k| 259k| ...  |-1.800902e-01 | 1.615240e-01 |    Inf
SCIP Status        : solving was interrupted [user interrupt]
Solving Time (sec) : 21469.69
Solving Nodes      : 1
Primal Bound       : +1.61523993625950e-01 (2 solutions)
Dual Bound         : -1.80090245701914e-01
=============================

I understand that it is a hard problem, but it is strange that solver did
not try to split bounded domain ! Only number of linear cuts has been
increasing...
It looks like SCIP only tries to approximate objective function epigraph by
polyhedron (as a result lower bound increases slowly).

Is it normal behaviour of SCIP or some settings for branching rules may be
applied ?

Sincerely yours,
-- 
Vladimir V. Voloshinov,
Ph.D, head of lab. C-3 "Distributed computing algorithms",
http://www.iitp.ru/ru/researchlabs/1040.htm,
Center for Distributed Computing, Institute for Information Transmission
Problems RAS, http://www.iitp.ru
web: our site is temporarily offline
<https://scholar.google.ru/citations?hl=en&user=-m4QhNEAAAAJ&view_op=list_works&sortby=pubdate>
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