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My main research
interest is the numerical optimization, particularly
design of efficient algorithms for finite or infinite
dimensional optimization problems. In virtually all branches
of engineering and industry, the search for optimality (cost,
energy, profits, ...) is challenging, because of the high
computational cost, the nonlinearity or the non-smoothness of
functions involved. I address these difficulties using
algorithms from duality theory and convex analysis (Aternating
Direction Method of Multiplier aka ADMM, Uzawa conjugate
gradient algorithm, primal-dual active set algorithm, Nesterov
algorithm, etc).
My research interests are in
all areas that intersect with numerical optimization including
operations research, computational mechanics, scientific
computing, parallel computing, high performance computing.
The algorithms are designed
and implemented using MATLAB/OCTAVE, C, FORTRAN or CUDA with
the aim to best fulfill the following scalability properties:
- the number of iterations is (virtually) independent of
the size of the problem;
- the CPU time is proportional to the size of the
problem.
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