Research Interests

My research interests include mathematical optimization, operations research, nonlinear dynamical systems and control theory. I am particularly interested in large-scale nonlinear optimization, semidefinite programming, moment methods, optimization under uncertainty, and applications of mathematical optimization to hard, nonlinear problems.

Educational Background

• Dr.Sc., Mathematical and Comp. Sciences, Tokyo Institute of Technology, 2010.
• M.Sc., Mathematics, ETH Zurich, 2007.

Refereed Publications

• “Moment and SDP relaxation techniques for smooth approximations of problems involving nonlinear differential equations“, M. Mevissen, J.B. Lasserre, D. Henrion, Proceedings of the 18th IFAC World Congress on Automatic Control (2011), pp. 10887-10892.
• “Exploiting Sparsity in Linear and Nonlinear Matrix Inequalities via Positive Semidefinite Matrix Completion“, S. Kim, M. Kojima, M. Mevissen, M. Yamashita, Mathematical Programming, 129 (2011), No. 1, pp. 33-68.
• “SDP Relaxations for Quadratic Optimization Problems Derived from Polynomial Optimization Problems“, M. Mevissen, M. Kojima, Asia-Pacific Journal of Operations Research, Asia-Pacific Journal of Operations Research, 27 (2010), No. 1, pp. 1-24.
• “Solutions of Polynomial Systems Derived from the Steady Cavity Flow Problem“, M. Mevissen, K. Yokoyama, N. Takayama, Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, pp. 255-262.
• “Solving partial differential equations via sparse SDP relaxations“, M. Mevissen, M. Kojima, J. Nie, and N. Takayama, Pacific Journal of Optimization, 4 (2008), No. 2, pp. 213-241.

Further Publications

• “Fast non-linear optimization for design problems on water networks“, B. Eck, M. Mevissen, World Environmental and Water Resources Congress 2013.
• “Valve Placement in Water Networks: Mixed Integer Non-Linear Optimization with Quadratic Pipe Friction“, B. Eck, M. Mevissen, September 2012, IBM Research Report (RC25307).
• “Mean squared error minimization for inverse moment problems“, D. Henrion, J.B. Lasserre, M. Mevissen, August 2012, Submitted.

Thesis

• "Sparse Semidefinite Programming Relaxations for Large Scale Polynomial optimization and their applications to differential equations", M. Mevissen, Doctoral Thesis, Tokyo Institute of Technology, 2010.

Presentations

• "Distributionally Robust Optimization for Polynomial Optimization Problems", 21st International Symposium on Mathematical Programming, Berlin, Germany, August 2012.
• "Nonlinear Optimization for Decision Problems in Water Distribution Networks under Uncertainty", 25th EURO Conference 2012, Vilnius, Lithuania, July 2012.
• "Moment Methods and SDP Relaxations for Nonconvex Problems", HPOPT 2012, Delft, Netherlands, June 2012.
• "Convex Optimization and MINLP Approaches for Decision Problems in Water Distribution Networks", INFORMS Optimization 2012, Coral Gables, February 2012.
• "Reconstruction of density functions by L2 norm minimization and semidefinite programming", OR 2011, Zurich, Switzerland, August 2011.
• "Moment and SDP relaxation methods for smooth approximations of nonlinear differential equations", SIAM Conference on Optimization, Darmstadt, Germany, May 2011.
• “Sparse SDP relaxation and moment methods for approximating solutions of nonlinear differential equations“, UC San Diego, October 2010.
• “Sparse SDP relaxations for Large Scale Polynomial Optimization and Applications to Differential Equations“, Tilburg University, Netherlands, June 2010.
• “Reduction of SDP relaxations for polynomial optimization problems“, 20th International Symposium on Mathematical Programming, Chicago, August 2009.
• “Solutions of Polynomial Systems Derived from the Steady Cavity Flow Problem“, International Symposium on Symbolic and Algebraic Computation, Seoul,July 2009.
• “Reduction techniques for SDP relaxations of polynomial optimization problems“, EURO Conference 2009, Bonn, July 2009.
• “Exploiting Sparsity in Nonlinear Matrix Inequalities and their SDP Relaxations“, 7th EUROPT Workshop Advances in Continuous Optimization, Remagen, July 2009.
• “Semidefinite programming techniques for solving nonlinear boundary value problems“, Conference on Optimization with interfaces and free boundaries, Regensburg, March 2009.
• “Nonconvex optimization methods for solving nonlinear differential equations“, Annual Meeting of the Mathematical Society of Japan, Tokyo, September 2008.
• “Semidefinite programming in polynomial and nonconvex quadratic optimization“, 4th Sino- Japanese Optimization Meeting, Tainan, Taiwan, August 2008.
• “Polynomial optimization techniques for second order PDEs and optimal control problems“, SIAM Conference on Optimization, Boston, May 2008.
• “Polynomial optimization techniques to solve nonlinear partial differential equations“, 2008 INFORMS Optimization conference, Atlanta, March 2008.
• “Solving partial differential equations via sparse SDP relaxations“, Workshop on Advances in Optimization, Tokyo Institute of Technology, April 2007.