I have applied both mathematical and evolutionary algorithms to solve my optimization problems.
Recently, I am working on an efficient optimization algorithm- alternating direction method of multipliers (ADMM). ADMM solves convex optimization problems by breaking them into smaller problems, each of which have closed form solution most of the time and therefore easier and faster to solve. ADMM is also very robust to algorithm parameters and shows excellent convergence characteristic for all positive values of its only parameter. ADMM also makes very little assumption on the property of the objective function and does not need the objective function to be differentiable .
ADMM applications:
Evolutionary algorithms:
I have improved as well as applied a wide variety of evolution algorithms. More specifically, my interest includes swarm intelligence, primarily I am focused on particle swarm optimization (PSO) algorithm and its variants. Some of my works on PSO are listed below:
Sparse Optimization (Sparse matrix separation):
Gross errors and missing values are common in measurement signals. I have applied sparse optimization techniques to separate the gross error and missing value matrix. Sample publications are listed below: