10. Further reading
Draft
The sidenotes of the earlier parts are the bibliography of this series. The table below is the shorter list: where to go next, by what the reader wants. The benchmark pages carry their dates, since their numbers change several times a year and a number quoted from them without its date cannot be interpreted. The purpose column follows the order of the series: the textbooks and surveys cover the ground of Sections 1 to 4, the global-solver and reformulation papers are the sources of Sections 4 and 5, the first-order, GPU and parallel rows belong to Sections 6 and 7, exact arithmetic to Section 5.6, and the tax-problem rows to Section 9; the libraries and benchmark pages are what Sections 5 and 8 measure against. Each entry ends with a phrase saying what it is good for, so the table can be read as a list of questions as well as a list of books.
| purpose | reading |
|---|---|
| textbooks | Boyd and Vandenberghe, Convex Optimization (Cambridge University Press, 2004), free online: the convex half |
| Nocedal and Wright, Numerical Optimization, 2nd ed. (Springer, 2006): what a local solver computes and certifies | |
| Wolsey, Integer Programming, 2nd ed. (Wiley, 2020): the integer half at textbook length | |
| Conforti, Cornuéjols and Zambelli, Integer Programming, GTM 271 (Springer, 2014): the integer half with proofs | |
| Horst and Tuy, Global Optimization: Deterministic Approaches, 3rd ed. (Springer, 1996), Chapter IV: why spatial B&B converges | |
| Locatelli and Schoen, Global Optimization: Theory, Algorithms, and Applications (MOS-SIAM, 2013): the continuous nonconvex case | |
| Tawarmalani and Sahinidis, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming (Kluwer, 2002): the book behind BARON | |
| Floudas, Nonlinear and Mixed-Integer Optimization (Oxford University Press, 1995): the process-systems view | |
| Lee and Leyffer (eds.), Mixed Integer Nonlinear Programming, IMA Volume 154 (Springer, 2012): the surveys of the 2008 workshop | |
| Grossmann, Advanced Optimization for Process Systems Engineering (Cambridge University Press, 2021): disjunctive programming | |
| Cornuéjols, Peña and Tütüncü, Optimization Methods in Finance, 2nd ed. (Cambridge University Press, 2018): the portfolio problems | |
| surveys | Belotti, Kirches, Leyffer, Linderoth, Luedtke and Mahajan, "Mixed-integer nonlinear optimization", Acta Numerica 22 (2013): the subject in 130 pages |
| Burer and Letchford, "Non-convex mixed-integer nonlinear programming: a survey", Surveys in Operations Research and Management Science 17 (2012): the nonconvex case | |
| Hemmecke, Köppe, Lee and Weismantel, "Nonlinear integer programming", in 50 Years of Integer Programming 1958–2008 (Springer, 2010), and Köppe, "On the complexity of nonlinear mixed-integer optimization", IMA 154 (2012): the complexity map | |
| Vielma, "Mixed integer linear programming formulation techniques", SIAM Review 57 (2015): formulations and their strength | |
| Kronqvist, Bernal, Lundell and Grossmann, "A review and comparison of solvers for convex MINLP", Optimization and Engineering 20 (2019): the convex solvers compared | |
| Puranik and Sahinidis, "Domain reduction techniques for global NLP and MINLP optimization", Constraints 22 (2017): bound tightening | |
| Mencarelli and D'Ambrosio, "Complex portfolio selection via convex mixed-integer quadratic programming: a survey", International Transactions in Operational Research 26 (2019): the portfolio MIQPs | |
| Bussieck and Vigerske, "MINLP solver software", Wiley Encyclopedia of Operations Research and Management Science (2011): the solvers | |
| Scavuzzo, Aardal, Lodi and Yorke-Smith, "Machine learning augmented branch and bound for mixed integer linear programming", Mathematical Programming 217 (2026), online 2024: learning in the tree | |
| Berthold, Heuristic Algorithms in Global MINLP Solvers, PhD thesis, TU Berlin (2014): the primal side | |
| Berthold, Lodi and Salvagnin, Primal Heuristics in Integer Programming (Cambridge University Press, 2025), and "Ten years of feasibility pump, and counting", EURO Journal on Computational Optimization 7 (2019): the primal side at book length | |
| Morrison, Jacobson, Sauppe and Sewell, "Branch-and-bound algorithms: a survey of recent advances in searching, branching, and pruning", Discrete Optimization 19 (2016): search, branching and pruning | |
| Cornuéjols, "Valid inequalities for mixed integer linear programs", Mathematical Programming 112 (2008): the Gomory, MIR and split cuts and their equivalences | |
| Frangioni, "About Lagrangian methods in integer optimization", Annals of Operations Research 139 (2005), and Guignard, "Lagrangean relaxation", TOP 11 (2003): Lagrangian bounds and decomposition | |
| Neumaier, "Complete search in continuous global optimization and constraint satisfaction", Acta Numerica 13 (2004): complete search, interval methods and rigour | |
| Laurent, "Sums of squares, moment matrices and optimization over polynomials", in Emerging Applications of Algebraic Geometry, IMA Volumes 149 (Springer, 2009), and Lasserre, An Introduction to Polynomial and Semi-Algebraic Optimization (Cambridge University Press, 2015): the moment hierarchy | |
| Lodi and Zarpellon, "On learning and branching: a survey", TOP 25 (2017): learning to branch, before the graph networks | |
| global solvers | Tawarmalani and Sahinidis, "A polyhedral branch-and-cut approach to global optimization", Mathematical Programming 103 (2005): BARON's polyhedral design |
| Kılınç and Sahinidis, "Exploiting integrality in the global optimization of mixed-integer nonlinear programming problems with BARON", Optimization Methods and Software 33 (2018): BARON and integrality | |
| Vigerske and Gleixner, "SCIP: global optimization of mixed-integer nonlinear programs in a branch-and-cut framework", Optimization Methods and Software 33 (2018): SCIP's design | |
| Bestuzheva, Chmiela, Müller, Serrano, Vigerske and Wegscheider, "Global optimization of mixed-integer nonlinear programs with SCIP 8", Journal of Global Optimization 91 (2025): SCIP 8 | |
| Hojny et al., "The SCIP Optimization Suite 10.0", arXiv 2511.18580 (2025): the exact mode is its Section 3.1 | |
| Belotti, Lee, Liberti, Margot and Wächter, "Branching and bounds tightening techniques for non-convex MINLP", Optimization Methods and Software 24 (2009): Couenne, branching, bound tightening | |
| Misener and Floudas, "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations", Journal of Global Optimization 59 (2014): ANTIGONE | |
| Belotti, Berthold, Gally, Gottwald and Pólik, "Solving MINLPs to global optimality with FICO Xpress Global", Optimization Online (July 2025): Xpress Global and its ablations | |
| Lundell, Kronqvist and Westerlund, "The supporting hyperplane optimization toolkit for convex MINLP", Journal of Global Optimization 84 (2022): SHOT | |
| Bongartz, Najman, Sass and Mitsos, "MAiNGO – McCormick-based Algorithm for mixed-integer Nonlinear Global Optimization", technical report, AVT.SVT, RWTH Aachen University (2018): MAiNGO | |
| reformulation | Günlük and Linderoth, "Perspective reformulations of mixed integer nonlinear programs with indicator variables", Mathematical Programming 124 (2010): the perspective and when it is the hull |
| Frangioni and Gentile, "Perspective cuts for a class of convex 0–1 mixed integer programs", Mathematical Programming 106 (2006), and "SDP diagonalizations and perspective cuts for a class of nonseparable MIQP", Operations Research Letters 35 (2007): perspective cuts, SDP diagonals | |
| Zheng, Sun and Li, "Improving the performance of MIQP solvers for quadratic programs with cardinality and minimum threshold constraints: a semidefinite program approach", INFORMS Journal on Computing 26 (2014): the SDP-chosen split | |
| Bertsimas, Cory-Wright and Pauphilet, "A unified approach to mixed-integer optimization problems with logical constraints", SIAM Journal on Optimization 31 (2021): the ridge dual | |
| Bertsimas and Cory-Wright, "A scalable algorithm for sparse portfolio selection", INFORMS Journal on Computing 34 (2022): 3,200 securities with certificates | |
| Lubin, Vielma and Zadik, "Mixed-integer convex representability", Mathematics of Operations Research 47 (2022): what is representable at all | |
| how far solvers came | Koch, Berthold, Pedersen and Vanaret, "Progress in mathematical programming solvers from 2001 to 2020", EURO Journal on Computational Optimization 10 (2022): 2001 against 2020 |
| Bixby, Fenelon, Gu, Rothberg and Wunderling, "Mixed-integer programming: a progress report", in The Sharpest Cut (MPS-SIAM, 2004), and Achterberg and Wunderling, "Mixed integer programming: analyzing 12 years of progress", in Facets of Combinatorial Optimization (Springer, 2013): the component ablations | |
| first-order LP, GPUs | Applegate, Díaz, Hinder, Lu, Lubin, O'Donoghue and Schudy, "Practical large-scale linear programming using primal-dual hybrid gradient", NeurIPS 2021, and "PDLP: a practical first-order method for large-scale linear programming", Mathematical Programming Computation (2026): PDLP |
| Applegate, Hinder, Lu and Lubin, "Faster first-order primal-dual methods for linear programming using restarts and sharpness", Mathematical Programming 201 (2023): restarts and sharpness | |
| Lu, Peng and Yang, "cuPDLPx: a further enhanced GPU-based first-order solver for linear programming", arXiv 2507.14051 (2025): cuPDLPx | |
| Lu and Yang, "A practical and optimal first-order method for large-scale convex quadratic programming", Mathematical Programming 215 (2026): PDQP, the quadratic case | |
| Blin, Gualandi, Maes, Lodi and Stellato, "Batched first-order methods for parallel LP solving in MIP", arXiv 2601.21990 (2026): batched first-order methods inside a tree | |
| Neumaier and Shcherbina, "Safe bounds in linear and mixed-integer linear programming", Mathematical Programming 99 (2004): safe bounds from any dual vector | |
| NLP on GPUs | Pacaud, Shin, Montoison, Schanen and Anitescu, "Condensed interior-point methods for scalable nonlinear programming on GPUs", Mathematical Programming Computation (2026), and Shin, Anitescu and Pacaud, "Accelerating optimal power flow with GPUs: SIMD abstraction of nonlinear programs and condensed-space interior-point methods", Electric Power Systems Research 236 (2024): the condensed KKT system |
| GPU bounding | Zhang, Kerkenhoff, Kichler, Dahmen, Mitsos, Naumann and Bongartz, "Accelerating deterministic global optimization via GPU-parallel interval arithmetic", arXiv 2507.20769 (2025): partitioned interval bounds |
| Gottlieb, Xu and Stuber, "Automatic source code generation for deterministic global optimization with parallel architectures", Optimization Methods and Software 41 (2026): generated McCormick kernels and ParBB | |
| parallel B&B | Lai and Sahni, "Anomalies in parallel branch-and-bound algorithms", Communications of the ACM 27 (1984): the anomalies |
| Gendron and Crainic, "Parallel branch-and-bound algorithms: survey and synthesis", Operations Research 42 (1994): the taxonomy of parallel branch and bound | |
| Ralphs, Shinano, Berthold and Koch, "Parallel solvers for mixed integer linear optimization", in Handbook of Parallel Constraint Reasoning (Springer, 2018): the current survey of MILP parallelism | |
| Shinano, Achterberg, Berthold, Heinz, Koch and Winkler, "Solving open MIP instances with ParaSCIP on supercomputers using up to 80,000 cores", IPDPS 2016, and "Solving previously unsolved MIP instances with ParaSCIP on supercomputers by using up to 80,000 cores", ZIB-Report 20-16 (2020): ParaSCIP | |
| Shinano, Heinz, Vigerske and Winkler, "FiberSCIP — a shared memory parallelization of SCIP", INFORMS Journal on Computing 30 (2018): FiberSCIP and its deterministic mode | |
| Gmys, "Exactly solving hard permutation flowshop scheduling problems on peta-scale GPU-accelerated supercomputers", INFORMS Journal on Computing 34 (2022), and Helbecque, Krishnasamy, Carneiro, Melab and Bouvry, "Portable PGAS-based GPU-accelerated branch-and-bound algorithms at scale", Concurrency and Computation: Practice and Experience 37 (2025): B&B on GPUs at scale | |
| Demmel and Nguyen, "Parallel reproducible summation", IEEE Transactions on Computers 64 (2015), and Ahrens, Demmel and Nguyen, "Algorithms for efficient reproducible floating point summation", ACM Transactions on Mathematical Software 46 (2020): reproducible summation | |
| exact arithmetic | Cook, Koch, Steffy and Wolter, "A hybrid branch-and-bound approach for exact rational mixed-integer programming", Mathematical Programming Computation 5 (2013); Eifler and Gleixner, "A computational status update for exact rational mixed integer programming", Mathematical Programming 197 (2023); Cheung, Gleixner and Steffy, "Verifying integer programming results", IPCO 2017: exact MIP and the VIPR certificate |
| the tax problem | Moehle, Kochenderfer, Boyd and Ang, "Tax-aware portfolio construction via convex optimization", Journal of Optimization Theory and Applications 189 (2021): the formulation, the two-stage method, 744 instances |
| Moehle, Gindi, Boyd and Kochenderfer, "Portfolio construction as linearly constrained separable optimization", Optimization and Engineering 24 (2023), arXiv 2103.05455: the ADMM heuristic and its convex-envelope bound | |
| Udell and Boyd, "Bounding duality gap for separable problems with linear constraints", Computational Optimization and Applications 64 (2016): the duality-gap theorem (Theorem 5.4.8) | |
| Lobo, Fazel and Boyd, "Portfolio optimization with linear and fixed transaction costs", Annals of Operations Research 152 (2007): fixed transaction costs and their envelope | |
| Boyd, Busseti, Diamond, Kahn, Koh, Nystrup and Speth, "Multi-period trading via convex optimization", Foundations and Trends in Optimization 3 (2017): multi-period trading | |
| 26 U.S.C. §§1012, 1091, 1211, 1212, 1222, 1223, 1411; 26 CFR §§1.1012-1, 1.1091-1; IRS Publication 550 (read 5 October 2026) | |
| libraries | MINLPLib, minlplib.org (Bussieck, Drud and Meeraus, "MINLPLib—a collection of test models for mixed-integer nonlinear programming", INFORMS Journal on Computing 15 (2003)); CSV export read 5 October 2026: 1,633 instances, latest addition 18 March 2026, 538 with a gap above 1e-4 |
| QPLIB, qplib.zib.de (Furini et al., "QPLIB: a library of quadratic programming instances", Mathematical Programming Computation 11 (2019)) | |
| MIPLIB 2017, miplib.zib.de (Gleixner et al., "MIPLIB 2017: data-driven compilation of the 6th mixed-integer programming library", Mathematical Programming Computation 13 (2021)) | |
| benchmarks, with their run dates | Mittelmann, plato.asu.edu/bench.html (index read 5 October 2026); MINLP: ftp/minlp.html (26 February 2026) with ftp/compare.txt (6 March 2026); binary nonconvex QPLIB: ftp/qplib.html (9 May 2026); discrete non-binary nonconvex QPLIB: ftp/nonbinary.html (12 May 2026); continuous nonconvex QPLIB: ftp/cnconv.html (17 May 2026; not quoted, see Section 8.7); convex discrete QPLIB: ftp/convex.html (7 September 2026); MISOCP: ftp/misocp.html (10 September 2026); QUBO: ftp/qubo.html (21 September 2026); LP feasibility, also GPUs: ftp/lpfeas.html (16 September 2026); MIP feasibility: ftp/mipfeas.html (16 September 2026); sparse SDP, also GPUs: ftp/sparse_sdp.html (1 October 2026); talks: plato.asu.edu/talks/informs2025.pdf (28 October 2025) and plato.asu.edu/talks/hongkong26.pdf (March 2026) |
| Bussieck and Dirkse, "Expanding the focus: introducing the MIPFEAS benchmark", gams.com/blog, 17 March 2026, updated 16 September 2026 | |
| MIP 2026 computational competition, "GPU-accelerated primal heuristics for MIP", mixedinteger.org/2026/competition |