Although both are gradient based optimization techniques, LBFGSB doesn't handle multiple objectives and hard constraints as SLSQP does.
Then this question comes naturally: why should you compare them, if they have been developed in order to attack different types of problems? :-)
There's this argument of using L-BFGS-B w/ other objectives as weak constraints, or as penalty terms but allows one to use only one objective function. Whereas, the SQP methods would require gradient computations for multiple objectives and require as many times computational times. A typical gradient computation using Adjoint methods for the problems I deal with takes almost 70 minutes on 1024 cores, and hence it's imperative that such comparisons be made between the two methods before I resort to SQP for better optimization results at the cost of added computations.
Dear Misra,
You can find required some comparison following studies.
Karahan, H., Gurarslan, G., and Geem, Z. (2013). ”Parameter Estimation of the Nonlinear Muskingum Flood-Routing Model Using a Hybrid Harmony Search Algorithm.”J. Hydrol. Eng., 18(3), 352–360.
Karahan, H. (2014). ”Closure to “Parameter Estimation of the Nonlinear Muskingum Flood-Routing Model Using a Hybrid Harmony Search Algorithm” by Halil Karahan, Gurhan Gurarslan, and Zong Woo Geem.”J. Hydrol. Eng., 19(4), 847–853.
Karahan, H. (2014). ”Discussion of “Improved Nonlinear Muskingum Model with Variable Exponent Parameter” by Said M. Easa.”J. Hydrol. Eng., 19(10), 07014007.
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