Interior proximal methods and central paths for convex second-order cone programming[J] . Shaohua Pan,Jein-Shan Chen.Nonlinear Analysis . 2010 (9)S. Pan and J.S. Chen. Interior proximal methods and central paths for convex second-order cone programming. Nonlinear Analysis: Theory, Methods & ...
最后这个非凸问题被转变成的形式为SOCP,因为解SOCP问题有成熟算法,解它十分有优势“poses the problem of minimum-fuel powered descent guidance as a second-order cone program (SOCP). This optimization problem can be solved in polynomial time using existing interior point method (IPM) algorithms that hav...
(QP) are convex optimization problems. Conic optimization problems, where the inequality constraints are convex cones, are also convex optimization problems. Problems with linear or convex quadratic objectives and linear and convex quadratic constraints (QCQP) can be represented as second-order cone ...
norm cone: {(x,t)| ∥x∥≤t}{(x,t)| ‖x‖≤t} euclidean norm cone is called second-order cone; norm balls and cones are convex polyhedra solution set of finitely many linear inequalities and equalities Ax⪯b, Cx=dAx⪯b, Cx=d (A∈Rm×n, C∈Rp×n, ⪯A∈Rm×n, C∈Rp...
8.2.3.2 Second-order cone programming model Second-order cone programming (SOCP) model is also a subfield of convex optimization. The SOCP model has recently taken great importance for OPF in DC grids since it is very efficient. In addition, it can solve this problem reliably and efficiently ...
How to convexify the intersection of a second order cone and a nonconvex quadratic. Mathematical Programming, 162(1):393-429, 2017.S. Burer and F. Kilin¸c-Karzan. How to convexify the intersection of a second order cone and a nonconvex quadratic. Technical report, Tepper School of ...
Second-order cone programming is a subclass of convex programming, and there are efficient second-order cone programming solvers with deterministic convergence properties. Consequently, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. 展开 ...
1.1 Linear programming (LP) and second-order cone programming (SOCP) Suppose we want to add \(\ell \) LP constraints of the form $$\begin{aligned} A_L^i x + b_L^i \ge 0, \ \ \ i\in \{1,\ldots ,\ell \}, \end{aligned}$$ (107) where \(A_L^i\) is an \(m_L...
总得来说凸优化问题有待解决,但是其中的几个子问题如second-order cone programming和geometric programming发展的比较成熟。 使用凸优化问题 和最小二乘和线性规划问题一样,核心都是如何识别或转化原问题为凸优化问题,这样就可以用成熟的技术解决。 非线性优化问题(TODO)...
For n=2, it was proved in [19] that every closed convex semialgebraic set K in the plane is second-order cone representable, i.e. has sxdeg(K)≤2. It can be shown that the bound sxdeg(K)≤⌊n2⌋+1 holds for the closed convex hull of an arbitrary semialgebraic curve S⊆...