Professor Butkovic's main research interest is the theory of max-linear systems, a rapidly evolving area of numerical linear algebra and applied discrete mathematics. He is the author of a research monograph on this subject published in 2010 and he is also the author or co-author of more than 40 peer-reviewed papers.
Peter Butkovic has received a number of grants in support of his research, including those from the EPSRC, LMS and Royal Society. He is the Chair of the LMS joint research group on tropical mathematics and its applications.
Peter has been in charge of a variety of modules such as Combinatorial Optimisation, Game Theory, Research Frontiers in Management Mathematics, Linear Programming, Non-Linear Programming and History of Mathematics. He supervises MSci projects and postgraduate students.
More information can be found on http://web.mat.bham.ac.uk/P.Butkovic/
Butkovič, P., Schneider, H. and Sergeev, S., Recognising weakly stable matrices, to appear in SIAM J. Control and Optimization.
Butkovič, P., Schneider, H. and Sergeev, S. (2012), Z-matrix equations in max algebra, nonnegative linear algebra and other semirings, Linear and Multilinear Algebra: 1-20.
Butkovič, P. (2010), Max-linear Systems: Theory and Algorithms, Springer Monographs in Mathematics, Springer-Verlag.
Sergeev, S., Schneider, H. and Butkovič, P. (2009), On visualisation scaling, subeigenvectors and Kleene stars in max algebra, Linear Algebra and its Applications 431: 2395–2406
Butkovič, P., Cuninghame-Green, R.A.and Gaubert, S. (2009), Reducible spectral theory with applications to the robustness of matrices in max-algebra, SIAM Journal on Matrix Analysis and Applications 31(3): 1412-1431
Butkovič, P. and Aminu, A. (2009), Max-linear programming. IMA Journal of Management Mathematics 20(3): 1-17
Butkovič, P. (2008), Finding a bounded mixed-integer solution to a system of dual inequalities, Operations Research Letters 36: 623-627
Butkovič, P. (2008), Permuted max-algebraic (tropical) eigenvector problem is NP-complete. Linear Algebra and its Applications 428: 1874-1882
Butkovič, P. and Cuninghame-Green, R.A. (2007), The eigenproblem for matrix powers in max-algebra, Linear Algebra and Its Applications 421: 370-381
Butkovič, P., Schneider, H. and Sergeev, S. (2007), Generators, extremals and bases of max cones, Linear Algebra and Its Applications 421: 394-406
Butkovič, P. and Schneider, H. (2005), Applications of max-algebra to diagonal scaling of matrices, Electronic Journal of Linear Algebra 13: 262-273
Burkard, R.E. and Butkovič, P. (2003), Max algebra and the linear assignment problem, Mathematical Programming, Ser.B 98: 415-429
Cuninghame-Green, R.A. and Butkovič, P. (2003), The equation Ax = By over (max, +), Theoretical Computer Science 293: 3-12
Butkovič, P. (2003), Max-algebra: the linear algebra of combinatorics? Linear Algebra and Its Applications 367: 313-335
Burkard, R.E. and Butkovič, P. (2003), Finding all essential terms of a characteristic maxpolynomial, Discrete Applied Mathematics 130: 367-380
Butkovič, P. (2000), The simple image set of (max, +) linear mappings, Discrete Applied Mathematics 105: 73-86