二阶锥规划(Second Order Cone Program, SOCP)是一种特殊的凸优化问题,它包含线性目标函数和由线性等式与不等式以及二阶锥不等式构成的约束。 SOCP结合了线性规划(LP)和二次规划(QP)的一些特点,但提供了更广泛的建模能力,特别是在处理涉及范数、距离和角度`的问题时。 SOCP的标准形式 一个典型的SOCP问题可以表述...
Application of second-order cone programming, Miguel SousaLoboa, LievenVandenbergheb, StephenBoydc, HervéLebretd. 因为我对socp研究不多,主要还是工作中确实没有很多处理socp的case,不过最近在处理一些问题,有明确的socp形式,所以进行了一波调研,后面再进行一波整理。本文是一个讲socp应用的经典文献,前半部分讲了...
二阶锥不等式(Second-Order Cone Inequality)是二阶锥规划(Second-Order Cone Programming, SOCP)中的核心组成部分。 二阶锥规划是一种凸优化问题,其中的约束条件包括线性不等式和或二阶锥不等式。二阶锥不等式的基本形式可以表示为: 这里, 表示向量 的欧几里得范数(即 $x$ 的长度),而 是一个标量。这个不等式...
Second-OrderConeProgramming F.Alizadeh ∗ D.Goldfarb † January14,2002 1Introduction Second-orderconeprogramming(SOCP)problemsareconvexoptimization problemsinwhichalinearfunctionisminimizedovertheintersectionofanaffine linearmanifoldwiththeCartesianproductofsecond-order(Lorentz)cones.Lin- earprograms,convexquadr...
Product-form cholesky factorization in interior point methods for second-order cone programming. Mathematical Programming, 103(1):153–179, 2005. [6] Luo, Zhi-Quan, Jos F. Sturm, and Shuzhong Zhang. Duality and Self-Duality for Conic Convex Programming. (1996). [7] Mehrotra, Sanjay. “On...
A second-order cone function (SOCF) is a function that can be written as (1) with parameters , , , and . In second-order cone programming, a linear function of x is minimized subject to one or more second-order cone constraints, along with the constraint Fx = g, where and . The...
1. 二阶锥 1.1 二阶锥定义 在此之前,先给出二阶锥的定义。 在kkk 维空间中二阶锥 (Second-order cone) 的定义为 Ck={[ut]∣u∈Rk−1,t∈R,∥u∥≤t} \mathcal{C}_{k}=\left\{\left[\begin{array}{l} {u} \\ {t} \end{array}\right] | u \in \mathbb{R}^{k-1}, t \in点...
At Mark 27, nAG have introduced new mathematical optimization solvers for Second-order Cone Programming, Derivative-free Optimization and First-order Active-set method. In addition to the new optimization solvers, the nAG Library Mark 27 features new routines for Nearest Correlation Matrix, Non-...
Eric Chu (Python interface, unit tests) Stephen Boyd (methods and maths) Michael Grant (CVX interface) Johan Löfberg (YALMIP interface) João Felipe Santos, Iain Dunning (Julia inteface) Han Wang (ECOS branch and bound wrapper) Santiago Akle (Exponential cone method and extension) ...
Optimal approximate design using second-order cone programmingRadoslav HarmanLenka Filova