Everything about Second-order cone programming

🧭 Start here: a 6-step reading path

1. Read the overview: Second-order cone programmingA 5-minute orientation
2. Skim a recent paper: UAV Collision Avoidance Using Mixed-Integer Second-Order Cone ProgrammingInfluential work since 2022
3. Pick up a classic book: Modeling and Optimization: Theory and ApplicationsThe most-reprinted book on the subject
4. Read the landmark paper: Applications of second-order cone programmingCited 1,940 times
5. Go sideways: Quadratically constrained quadratic programA closely related topic
6. Go sideways: Interior-point methodA closely related topic

🏆 Landmark papers (most cited)

• Applications of second-order cone programming

  Miguel Sousa Lobo, Lieven Vandenberghe, Stephen Boyd · 1998 · Linear Algebra and its Applications · 1,940 citations

• Second-order cone programming

  F. Alizadeh, D. Goldfarb · 2003 · Mathematical Programming · 1,192 citations

• Entry Trajectory Optimization by Second-Order Cone Programming

  Xinfu Liu, Zuojun Shen, Ping Lu · 2016 · Journal of Guidance, Control, and Dynamics · 335 citations

• Second‐Order Cone Programming Relaxation of Sensor Network Localization

  Paul Tseng · 2007 · SIAM Journal on Optimization · 177 citations

• Perturbation analysis of second-order cone programming problems

  J. Frédéric Bonnans, Héctor Ramírez C. · 2005 · Mathematical Programming · 128 citations

• Second order cone programming relaxation of nonconvex quadratic optimization problems

  Sunyonga Kim, Masakazu Kojima · 2001 · Optimization Methods and Software · 91 citations

• Computational Cam clay plasticity using second-order cone programming

  K. Krabbenhoft, A.V. Lyamin · 2012 · Computer Methods in Applied Mechanics and Engineering · 75 citations

• Robust array interpolation using second-order cone programming

  M. Pesavento, A.B. Gershman, Zhi-Quan Luo · 2002 · IEEE Signal Processing Letters · 50 citations

🆕 Influential since 2022

• UAV Collision Avoidance Using Mixed-Integer Second-Order Cone Programming

  Guoxu Zhang, Xinfu Liu · 2022 · Journal of Guidance, Control, and Dynamics · 30 citations

• UAV trajectory optimization using chance-constrained second-order cone programming

  Xin Sun, Baihai Zhang, Runqi Chai · 2022 · Aerospace Science and Technology · 22 citations

• Fully Distributed Second-Order Cone Programming Model for Expansion in Transmission and Distribution Networks

  Jia Liu, Zao Tang, Peter Pingliang Zeng · 2022 · IEEE Systems Journal · 20 citations

• Descent Property in Sequential Second-Order Cone Programming for Nonlinear Trajectory Optimization

  Lei Xie, Xiang Zhou, Hong-Bo Zhang · 2023 · Journal of Guidance, Control, and Dynamics · 17 citations

• SONC optimization and exact nonnegativity certificates via second-order cone programming

  Victor Magron, Jie Wang · 2023 · Journal of Symbolic Computation · 15 citations

📚 Books worth reading

• Modeling and Optimization: Theory and ApplicationsTamás Terlaky · 2012
• A TOUR OF THE WORLDMalik Mansab Khan, Muhammad Rafique Abdul Aziz · 2025

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

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• Spectrahedron In convex geometry, a spectrahedron is a shape that can be represented as a linear matrix inequality. Alternatively, the set of n × n positive semidefinite…
• MOSEK MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constrained, conic and…
• Sum-of-squares optimization A sum-of-squares optimization program is an optimization problem with a linear cost function and constraints that certain polynomials constructed from…
• Nonlinear programming In mathematics, nonlinear programming (NLP), also known as nonlinear optimization, is the process of solving an optimization problem where some of the…