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Conic optimization is a generalization of linear optimization. My research in this area is concerned with improving models and algorithms for the application of conic optimization to hard engineering optimization problems of a combinatorial nature.
The main objective is to use conic optimization in order to obtain not only good solutions, but also tight bounds on the objective value of the unknown global optimal solution, which are essential to estimate the quality of the solutions found. These ingredients are the key to developing more efficient algorithms for solving these hard problems.
Book
- M.F. Anjos and J.B. Lasserre, Eds. Handbook of Semidefinite, Conic and Polynomial Optimization: Theory, Algorithms, Software and Applications. International Series in Operational Research and Management Science. Volume 166, 2012. ISBN 978-1-4614-0768-3
Book Chapters
- E. Adams and M.F. Anjos. Exact Separation of k-Projection Polytope Constraints. Accepted for publication in: Modeling and Optimization: Theory and Applications, M. Takáč et al. (eds.)
- M.F. Anjos. Conic Optimization. In: Advances and Trends in Optimization with Engineering Applications, T. Terlaky, M.F. Anjos, and S. Ahmed (eds.), SIAM, 2017, 107-120
- M.F. Anjos, B. Ghaddar, L. Hupp, F. Liers, and A. Wiegele. Solving k-way Graph Partitioning Problems to Optimality: The Impact of Semidefinite Relaxations and the Bundle Method (invited chapter). In: Facets of Combinatorial Optimization - Festschrift for Martin Grötschel, M. Jünger and G. Reinelt (eds.), Springer, 2013, 355-386
- M.F. Anjos, F. Liers, G. Pardella, and A. Schmutzer. Engineering Branch-and-Cut Algorithms for the Equicut Problem (invited chapter). In: Discrete Geometry and Optimization, A. Deza, K. Bezdek and Y.Ye (eds.), Fields Institute Communications, Vol. 69, Springer, 2013, 17-32
- M.F. Anjos. Progress in Semidefinite Optimization Techniques for Satisfiability. In: Progress in Combinatorial Optimization, A.R. Mahjoub (ed), Wiley-ISTE, 2012
- M.F. Anjos and J.B. Lasserre. Introduction to Semidefinite, Conic and Polynomial Optimization. In: Handbook on Semidefinite, Cone and Polynomial Optimization, M.F. Anjos and J.B. Lasserre (eds), International Series in Operations Research & Management Science, Frederick S. Hilier (ed.), Springer, 2012, 1-22
- A. Engau, M.F. Anjos, and A. Vannelli. A Primal-Dual Slack Approach to Warmstarting Interior-Point Methods for Linear Programming. In: Operations Research and Cyber-Infrastructure, J.W. Chinneck, B. Kristjansson, M.J. Saltzman (eds), Springer-Verlag, 2009, 195-217
Research Articles
- V.J.R. de Sousa, M.F. Anjos, and S. Le Digabel. Computational Study of Valid Inequalities for the Maximum k-Cut Problem. To appear in Annals of Operations Research
- A. Engau and M.F. Anjos. A Primal-Dual Interior-Point Algorithm for Linear Programming with Selective Addition of Inequalities. To appear in Optimization
- M.F. Anjos and M.V.C. Vieira. On Semidefinite Least Squares and Minimum Unsatisfiable Subformulas. Discrete Applied Mathematics, 217(2), 2017, 79-96
- E. Adams, M.F. Anjos, F. Rendl, and A. Wiegele. A Hierarchy of Subgraph Projection-Based Semidefinite Relaxations for some NP-Hard Graph Optimization Problems. INFOR, 53(1), 2016, 40-48
- B. Ghaddar, J.C. Vera, and M.F. Anjos. A Dynamic Inequality Generation Scheme for Polynomial Programming. Mathematical Programming, 156(1), 2016, 21-57
- M.F. Anjos, X.-W. Chang, and W.-Y. Ku. Lattice Preconditioning for the Real Relaxation Branch-and-Bound Approach for Integer Least Squares Problems. Journal of Global Optimization, 59(2-3), 2014, 227-242
- M.F. Anjos and M.V.C. Vieira. Semidefinite Resolution and Exactness of Semidefinite Relaxations for Satisfiability. Discrete Applied Mathematics, 161, 2013, 2812-2826
- A. Engau, M.F. Anjos, and I.M. Bomze. Constraint Selection in a Build-Up Interior-Point Cutting-Plane Method for Solving Relaxations of the Stable-Set Problem. Mathematical Methods of Operations Research, 78, 2013, 35-59
- A. Engau, M.F. Anjos, and A. Vannelli. On Handling Cutting Planes in Interior-Point Methods for Solving Semidefinite Relaxations of Binary Quadratic Optimization Problems. Optimization Methods and Software, 27(3), 2012, 539-559
- I. Jankovits, C. Luo, M.F. Anjos, and A. Vannelli. A Convex Optimisation Framework for the Unequal-Areas Facility Layout Problem. European Journal of Operational Research, 214(2), 2011, 199-215
- A. Alfakih, M.F. Anjos, V. Piccialli, and H. Wolkowicz. Euclidean Distance Matrices, Semidefinite Programming, and Sensor Network Localization. Portugaliae Mathematica, 68(1), 2011, 53102 (invited survey)
- B. Ghaddar, J.C. Vera, and M.F. Anjos. Second-Order Cone Relaxations for Binary Quadratic Polynomial Programs. SIAM Journal on Optimization, 21(1), 2011, 391-414
A. Engau, M.F. Anjos, and A. Vannelli. On Interior-Point Warmstarts for Linear and Combinatorial Optimization. SIAM Journal on Optimization, 20(4), 2010, 1828-1861.
This paper earned Engau the 2009 MITACS Best Student Paper Award.
- A. Engau, M.F. Anjos, and A. Vannelli. An Improved Interior-Point Cutting-Plane Method for Binary Quadratic Optimization. Electronic Notes in Discrete Mathematics, 36, 2010, 743-750
- M.F. Anjos and G. Yen. Provably Near-Optimal Solutions for Very Large Single-Row Facility Layout Problems (invited paper). Optimization Methods and Software, 24(4), 2009, 805-817
B. Ghaddar, M.F. Anjos, and F. Liers. A Branch-and-Cut Algorithm Based on Semidefinite Programming for the Minimum k-Partition Problem. Annals of Operations Research, 188(1), 2011, 155-174.
This paper earned Ghaddar the 2008 Fraser Research Prize for the Best Research Paper by a graduate student in Management Sciences at the University of Waterloo.
- M.F. Anjos and A. Vannelli. Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes. INFORMS Journal on Computing, 20(4), 2008, 611-617
- M.F. Anjos. An Extended Semidefinite Relaxation for Satisfiability. Journal on Satisfiability, Boolean Modeling and Computation, 4, 2007, 15-31
- M.F. Anjos and S. Burer. On Handling Free Variables in Interior-Point Methods for Conic Linear Optimization. SIAM Journal on Optimization, 18(4), 2007, 1310-1325
- M.F. Anjos. An Explicit Semidefinite Characterization of Satisfiability for Tseitin Instances on Toroidal Grid Graphs. Annals of Mathematics and Articial Intelligence, 48(1-2), 2006, 1-14
- M.F. Anjos, A. Kennings, and A. Vannelli. A Semidefinite Optimization Approach for the Single-Row Layout Problem with Unequal Dimensions. Discrete Optimization, 2(2), 2005, 113-122.
This paper was a Top Cited Paper in the journal Discrete Optimization for the period 2005-2010.
- M.F. Anjos. Semidefinite Optimization Approaches for Satisfiability and Maximum-Satisfiability Problems. Journal on Satisfiability, Boolean Modeling and Computation, 1, 2005, 1-47 (invited survey).
- M.F. Anjos. An Improved Semidefinite Programming Relaxation for the Satisfiability Problem. Mathematical Programming, 102(3), 2005, 589-608
- M.F. Anjos. On Semidefinite Programming Relaxations for the Satisfiability Problem. Mathematical Methods of Operations Research, 60(3), 2004, 349-367
- H. Wolkowicz and M.F. Anjos. Semidefinite Programming for Discrete Optimization and Matrix Completion Problems. Discrete Applied Mathematics, 123(1-3), 2002, 513-577
- M.F. Anjos and H. Wolkowicz. Strengthened Semidefinite Relaxations via a Second Lifting for the Max-Cut Problem. Discrete Applied Mathematics, 119(1-2), 2002, 79-106
- M.F. Anjos and H. Wolkowicz. Geometry of Semidefinite Max-Cut Relaxations via Matrix Ranks. Journal of Combinatorial Optimization, 6(3), 2002, 237-270
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