ECOS is an open-source numerical software package for solving optimization problems with second-order cone constraints (SOCPs). This includes linear (LPs), quadratic (QPs), and quadratically-constrained quadratic programs (QCQPs). ECOS also supports a small number of binary or integer variables by employing a simple branch and bound technique. ECOS is written entirely in ANSI C and does not depend on dedicated libraries for the required linear algebra computations operating on the (sparse) problem data. As a consequence, it can be used to solve optimization problems on any embedded system for which a C-compiler is available. The implemented solution algorithm is an interior-point method that is an efficient standard algorithm for solving convex optimization problems. It uses regularization and iterative refinement techniques to be numerically robust. The solution methods have been developed in cooperation with Prof. Stephen Boyd of Stanford University. A number of helpful contributors have provided interfaces to the following programming and modeling languages: CVX (Michael Grant), YALMIP (Johan Löfberg), Julia (João Felipe Santos, Iain Dunning, Anthony Kelman)

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  1. Capatti, Zeno; Hirschi, Valentin; Kermanschah, Dario; Pelloni, Andrea; Ruijl, Ben: Numerical loop-tree duality: contour deformation and subtraction (2020)
  2. Coey, Chris; Lubin, Miles; Vielma, Juan Pablo: Outer approximation with conic certificates for mixed-integer convex problems (2020)
  3. Hütter, Jan-Christian; Mao, Cheng; Rigollet, Philippe; Robeva, Elina: Optimal rates for estimation of two-dimensional totally positive distributions (2020)
  4. Hütter, Jan-Christian; Mao, Cheng; Rigollet, Philippe; Robeva, Elina: Estimation of Monge matrices (2020)
  5. Lesage-Landry, Antoine; Shames, Iman; Taylor, Joshua A.: Predictive online convex optimization (2020)
  6. Liao-McPherson, Dominic; Kolmanovsky, Ilya: FBstab: a proximally stabilized semismooth algorithm for convex quadratic programming (2020)
  7. Liao-McPherson, Dominic; Nicotra, Marco M.; Kolmanovsky, Ilya: Time-distributed optimization for real-time model predictive control: stability, robustness, and constraint satisfaction (2020)
  8. McKinnon, Karen A.; Poppick, Andrew: Estimating changes in the observed relationship between humidity and temperature using noncrossing quantile smoothing splines (2020)
  9. Safarina, Sena; Moriguchi, Satoko; Mullin, Tim J.; Yamashita, Makoto: Conic relaxation approaches for equal deployment problems (2020)
  10. Takapoui, Reza; Moehle, Nicholas; Boyd, Stephen; Bemporad, Alberto: A simple effective heuristic for embedded mixed-integer quadratic programming (2020)
  11. Ahmadi, Amir Ali; Majumdar, Anirudha: DSOS and SDSOS optimization: more tractable alternatives to sum of squares and semidefinite optimization (2019)
  12. Busseti, Enzo; Moursi, Walaa M.; Boyd, Stephen: Solution refinement at regular points of conic problems (2019)
  13. Fawzi, Hamza; Saunderson, James; Parrilo, Pablo A.: Semidefinite approximations of the matrix logarithm (2019)
  14. Fu, Anqi; Ungun, Barıṣ; Xing, Lei; Boyd, Stephen: A convex optimization approach to radiation treatment planning with dose constraints (2019)
  15. Kian, Ramez; Berk, Emre; Gürler, Ülkü: Minimal conic quadratic reformulations and an optimization model (2019)
  16. Moehle, Nicholas; Shen, Xinyue; Luo, Zhi-Quan; Boyd, Stephen: A distributed method for optimal capacity reservation (2019)
  17. Nystrup, Peter; Boyd, Stephen; Lindström, Erik; Madsen, Henrik: Multi-period portfolio selection with drawdown control (2019)
  18. Tu, Shu; Defourny, Boris: An active-set strategy to solve Markov decision processes with good-deal risk measure (2019)
  19. Baldi, Simone; Papachristodoulou, Antonis; Kosmatopoulos, Elias B.: Adaptive pulse width modulation design for power converters based on affine switched systems (2018)
  20. Calès, Ludovic; Chalkis, Apostolos; Emiris, Ioannis Z.; Fisikopoulos, Vissarion: Practical volume computation of structured convex bodies, and an application to modeling portfolio dependencies and financial crises (2018)

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