Publications

Published papers

• (with D. Ek), A structured modified Newton approach for solving systems of nonlinear equations arising in interior-point methods for quadratic programming, Computational Optimization and Applications 86 (2023), 1–48.
• (with I. Bengtsson and A. Fredriksson), Implications of using the clinical target distribution as voxel-weights in radiation therapy optimization, Physics in Medicine & Biology 68 (2023), 095005.
• (with D. Ek), Exact linesearch limited-memory quasi-Newton methods for minimizing a quadratic function,  Computational Optimization and Applications 79 (2021), 789–816.
• (with D. Ek), Approximate solution of system of linear equations arising in interior-point methods for bound-constrained optimization, Computational Optimization and Applications 79 (2021), 155–191.
• (with F. Wang), On the existence of a short pivoting sequence for a linear program. Operations Research Letters 48 (2020), 697-702.
• (with E. Hagrot, H. Æ. Oddsdóttir, M. Mäkinen and V. Chotteau), Novel column generation-based optimization approach for poly-pathway kinetic model applied to CHO cell culture. Metabolic Engineering Communications 8 (2019), e00083.
• (with M. Böck and K. Eriksson), On the interplay between robustness and dynamic planning for adaptive radiation therapy. Biomedical Physics & Engineering Express 5 (2019), 045004.
• (with L. Engberg and K. Eriksson), Increased accuracy of planning tools for optimization of dynamic multileaf collimator delivery of radiotherapy through reformulated objective functions. Physics in Medicine & Biology 63 (2018) 125012. (Also available as arXiv:1802.00619 [math.OC])
• (with T. Odland), On exact linesearch quasi-Newton methods for minimizing a quadratic function. Computational Optimization and Applications 69 (2018), 225-241. (Also available as arXiv:1503.01892 [math.OC])
• (with M. Böck, K. Eriksson and B. Hårdemark), Towards robust adaptive radiation therapy strategies. Medical Physics 44 (2017), 2054-2065. (Also available as arXiv:1611.01399 [math.OC])
• (with L. Engberg, K. Eriksson and B. Hårdemark), Explicit optimization of plan quality measures in intensity-modulated radiation therapy treatment planning. Medical Physics 44 (2017) 2045-2053. (Also available as arXiv:1607.01148 [physics.med-ph])
• (with P. E. Gill and E. Wong), Primal and dual active-set methods for convex quadratic programming, Mathematical Programming 159 (2016), 469-508. (Also available as arXiv:1503.08349 [math.OC])
• (with H. Æ. Oddsdóttir, E. Hagrot and V. Chotteau), Robustness analysis of elementary flux modes generated by column generation, Mathematical Biosciences 273 (2016), 45-56. (Also available as arXiv:1503.03459 [math.OC])
• (with H. Æ. Oddsdóttir, E. Hagrot and V. Chotteau), On dynamically generating relevant elementary flux modes in a metabolic network using optimization. Journal of Mathematical Biology 71 (2015), 903-920. (Also available as arXiv:1410.2680 [math.OC])
• (with A. Fredriksson and B. Hårdemark), Maximizing the probability of satisfying the clinical goals in radiation therapy treatment planning under setup uncertainty, Medical Physics 42 (2015), 3992–3999.
• (with T. Odland), On the connection between the conjugate gradient method and quasi-Newton methods on quadratic problems. Computational Optimization and Applications 60 (2015), 377-392 . (Also available as arXiv:1407.1268 [math.OC])
• (with F. Carlsson), On column generation approaches for approximate solutions of quadratic programs in intensity-modulated radiation therapy. Annals of Operations Research 223 (2014), 471-481.
• (with R. Bokrantz), An algorithm for approximating convex Pareto surfaces based on dual techniques. INFORMS Journal on Computing 25 (2013), 377-393.
• (with A. Fredriksson and B. Hårdemark), Minimax optimization for handling range and setup uncertainties in proton therapy. Medical Physics 38 (2011), 1672-1684.
• (with P. E. Gill and J. D. Griffin), Iterative solution of augmented systems arising in interior methods. SIAM Journal on Optimization 18 (2007), 666-690.
• (with F. Carlsson, H. Rehbinder and K. Eriksson), Using eigenstructure of the Hessian to reduce the dimension of the intensity modulated radiation therapy optimization problem. Annals of Operations Research 148 (2006), 81-94.
• On warm starts for interior methods. In IFIP International Federation for Information Processing, volume 199, System Modeling and Optimization, eds. F. Ceragioli, A. Dontchev, H. Furuta, K. Marti, and L. Pandolfi, pp. 51-66. Springer, Boston, 2006.
• (with F. Carlsson), Iterative regularization in intensity-modulated radiation therapy optimization. Medical Physics 33 (2006), 225-234.
• (with P. E. Gill and M. H. Wright), Interior methods for nonlinear optimization. SIAM Review 44 (2002), 525-597.
• Inertia-controlling factorizations for optimization algorithms. Applied Numerical Mathematics 43 (2002), 91-107.
• (with M. Prytz), Dimensioning multicast-enabled communications networks. Networks 39 (2002), 216-231.
• (with G. Sporre), On weighted linear least-squares problems related to interior methods for convex quadratic programming. SIAM Journal on Matrix Analysis and Applications 23 (2001), 42-56.
• Optimality conditions for nonconvex semidefinite programming. Mathematical Programming 88 (2000), 105-128.
• (with P. E. Gill), Primal-dual interior methods for nonconvex nonlinear programming. SIAM Journal on Optimization 8 (1998), 1132-1152.
• (with W. Murray), Newton methods for large-scale linear inequality-constrained minimization. SIAM Journal on Optimization 7 (1997), 162-176.
• On linear least-squares problems with diagonally dominant weight matrices. SIAM Journal on Matrix Analysis and Applications 17 (1996), 763-788.
• (with P. E. Gill and J. R. Shinnerl), Stability of symmetric ill-conditioned systems arising in interior methods for constrained optimization. SIAM Journal on Matrix Analysis and Applications 17 (1996), 187-211.
• (with P. E. Gill and W. Murray), Computing modified Newton directions using a partial Cholesky factorization. SIAM Journal on Scientific Computing 16 (1995), 139-150.
• (with U. Ringertz), On the use of a modified Newton method for nonlinear finite element analysis. Computer Methods in Applied Mechanics and Engineering 110 (1993), 275-283.
• (with W. Murray), Newton methods for large-scale linear equality-constrained minimization. SIAM Journal on Matrix Analysis and Applications 14 (1993), 560-587.
• (with P. E. Gill and W. Murray), On the identification of local minimizers in inertia-controlling methods for quadratic programming. SIAM Journal on Matrix Analysis and Applications 12 (1991), 730-746.

Technical reports and preprints

• (with S. Peng, G. Canessa and D. Ek), Quasi-Newton methods for minimizing a quadratic function subject to uncertainty, arXiv:2109.00072 [math.OC], 2021.
• (with D. Ek), An optimization derivation of the method of conjugate gradients, arXiv:2011.02337 [math.OC], 2020.
• (with L. Engberg), On tradeoffs between treatment time and plan quality of volumetric-modulated arc therapy with sliding-window delivery, arXiv:1810.08610 [physics.med-ph], 2018.
• (with T. Odland), On solving symmetric systems of linear equations in an unnormalized Krylov subspace framework, arXiv:1409.4937 [math.OC], 2014.
• (with M. H. Wright), An elementary proof of linear programming optimality conditions without using Farkas' lemma, arXiv:1407.1240 [math.OC], 2014.
• (with A. Fredriksson and B. Hårdemark) Optimizing the scenario positions for robust radiation therapy treatment planning, Report TRITA-MAT-2012-OS5, Department of Mathematics, KTH Royal Institute of Technology, 2012.
• (with R. Bokrantz), A dual algorithm for approximating Pareto sets in convex multi-criteria optimization. Report TRITA-MAT-2011-OS3, Department of Mathematics, Royal Institute of Technology, 2011.
• (with M. Fallgren and G. Fodor), An optimization approach to joint cell, channel and power allocation in multicell networks. Report TRITA-MAT-2011-OS2, Department of Mathematics, Royal Institute of Technology, 2011.
• A sufficiently exact inexact Newton step based on reusing matrix information. Report TRITA-MAT-2009-OS7, Department of Mathematics, Royal Institute of Technology, 2009.
• An elementary proof of optimality conditions for linear programming. Report TRITA-MAT-2008-OS6, Department of Mathematics, Royal Institute of Technology, 2008.
• (with F. Carlsson), A conjugate-gradient based approach for approximate solutions of quadratic programs. Report TRITA-MAT-2008-OS2, Department of Mathematics, Royal Institute of Technology, 2008.
• On the behavior of the conjugate-gradient method on ill-conditioned problems. Report TRITA-MAT-2006-OS1, Department of Mathematics, Royal Institute of Technology, 2006.
• (with G. Sporre), Characterization of the limit point of the central path in semidefinite programming. Report TRITA-MAT-2002-OS12, Department of Mathematics, Royal Institute of Technology, 2002.
• (with G. Sporre), Relations between divergence of multipliers and convergence to infeasible points in primal-dual interior methods for nonconvex nonlinear programming. Report TRITA-MAT-2002-OS7, Department of Mathematics, Royal Institute of Technology, 2002.
• (with M. Prytz), Dimensioning of a multicast network that uses shortest path routing distibution trees. Report TRITA-MAT-2002-OS1, Department of Mathematics, Royal Institute of Technology, 2002.
• A note on maximum-smoothness approximation of forward interest rate. Report TRITA-MAT-1998-OS3, Department of Mathematics, Royal Institute of Technology, 1998.
• Newton methods for nonconvex optimization. Report TRITA-MAT-1990-10, Department of Mathematics, Royal Institute of Technology, 1990. (Doctoral thesis).
• (with P. E. Gill and W. Murray), A modified Newton method for unconstrained minimization. Report SOL 89-12, Department of Operations Research, Stanford University, 1989.