I installed JuMP and tried to initialize a Model(), while doing so I would like to specify the solver based on what is available. For this how could I get a list of available solvers?
The list of solvers currently supported by the julia optimisation eco-system is maintained on the juliaopt website: http://www.juliaopt.org/
At the time of writing, it included a long list of commercial and open source solvers:
Clp, Cbc, GLPK, ECOS, SCS, CPLEX, Gurobi, FICO Xpress, Mosek, NLopt, Ipopt, Bonmin, Couenne, Artelys Knitro
Note that each of these solvers come with their own Julia wrappers, which need to be installed in addition to installing the JuMP package. Pkg.add(Clp) will, for example, install the Clp Julia wrapper. For wrappers around open source solvers, such as Clp, the underlying solver will usually be downloaded and installed as part of the Julia package installation.
Obviously, for the commercial solvers, one needs to buy a license and install the solver program.