Research Projects (running or recently finished)

• EU FP7 project 313781 AMAZE - Additive Manufacturing Aiming at Zero Waste and Eco-Production, 2013-2017 (coordinator D. Jarvis, ESA)
• Variational and numerical analysis in nonsmooth continuum mechanics, Grant Agency of the Czech Republic project P201/12/0671, PI J. Haslinger, 2012-2014
• EU FP6 PLATO-N: A PLAtform for Topology Optimisation incorporating Novel, Large-Scale, Free Material Optimisation and Mixed Integer Programming Methods 2006-2009
  
• Bridging the Gap - Multi-Disciplinary Optimization and Data Mining at Birmingham, EPSRC funded, 2008-2011
  

Areas of Research

Active

• Algorithms for the solution of large (and sparse) mathematical optimization problems. These include 
• PENNON, a code for convex and nonconvex problems of nonlinear and semidefinite programming
• PENLAB a free open source MATLAB toolbox for nonlinear optimization, linear and nonlinear semidefinite optimization and any combination of these
• Multilevel and domain decomposition methods in constrained optimization

• Structural Optimization including
• material optimization of linear elastic bodies. This page also includes information about our code MOPED.
• truss optimization including single and multiple load topo or geo/topo design with displacement, stability and robustness constraints.
• shape optimizations of elastic bodies governed by variational inequalities.


• Mathematical Programs with Equilibrium Constraints (MPEC).

Past

• Numerical solution of large three-dimensional linear elasticity problems by means of adaptive mesh refinement and local multigrid method.
• An iterative method for linear complementarity problems

Software (some projects are being moved to github.com/kocvara)

• PENSDP, PENBMI, PENNON, codes for linear, bilinear and general problems of nonlinear and semidefinite programming
• PENLAB a free open source MATLAB toolbox for nonlinear optimization, linear and nonlinear semidefinite optimization and any combination of these
• SPARSE SDP, a library of sparse SDP problems from structural optimization (SDPA input format)
• MG_2d_public (zip file, 11.498 KB) MATLAB software accompanying the paper "M. Kocvara and S. Mohammed. A first-order multigrid method for bound-constrained convex optimization. Optimization Methods and Software 31(3):622-644, 2016. arXiv:1602.03771"