Is there any difference between the result for dual and primal of SVM? There are many variants of types of solver in liblinear. But, I am kind of wondering whether there will be any difference for primal and dual for L2-loss. They suppose to be different forms of the optimization. Will they give different results?
-s type : set type of solver (default 1)
  for multi-class classification
   0 -- L2-regularized logistic regression (primal)
   1 -- L2-regularized L2-loss support vector classification (dual)
   2 -- L2-regularized L2-loss support vector classification (primal)
...

 A: At worst, the resulting models should still be approximately equal since this is a convex optimization problem.
Their paper at JMLR1 mentions "LIBLINEAR implements a trust  region Newton method" for L2-SVM.
Reading the guide2, in Apendix C.3 the following problem is discussed:

C.3 Number of instances ≫ number of features
As the number of features is small, one often maps data to higher
  dimensional spaces (i.e., using  nonlinear  kernels). However,  if 
  you really  would  like  to  use  the  linear kernel, you may use
  LIBLINEAR with the option -s 2. When the number of features is small,
  it is often faster than the default -s 1. Consider the data
  [http://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/binary/covtype.libsvm.binary.scale.bz2].
  The number of instances 581,012 is much larger than the number of
  features 54. We run LIBLINEAR with -s 1 (default) and -s 2.
\$ time liblinear-1.21/train -c 4 -v 5 -s 2
  covtype.libsvm.binary.scale Cross Validation Accuracy = 75.67%
  67.224s
\$ time liblinear-1.21/train -c 4 -v 5 -s 1
  covtype.libsvm.binary.scale Cross Validation Accuracy = 75.6711%
  452.736s
Clearly, using -s 2 leads to shorter training time.

See the cross validation accuracy is approximately the same. So it's mostly a matter of training time.

[1] Fan, Rong-En, et al. "LIBLINEAR: A library for large linear classification." Journal of machine learning research 9.Aug (2008): 1871-1874.
[2] Hsu, Chih-Wei, Chih-Chung Chang, and Chih-Jen Lin. "A practical guide to support vector classification"(http://www.csie.ntu.edu.tw/~cjlin/papers/guide/guide.pdf." (2003).
