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凸优化笔记(4)Semi-Definite Programming简介 - 知乎 - 知乎专栏
控制理论求解的Linear matrix inequality(LMI)就是SDP问题。 用类似的方法可以推出QCQP(Quadratic Constrained Quadratic Programming)与SOCP(Second Order Conic Programing)是SDP的一种特殊情况,这里暂时不细讲( LP\subseteq convex{\kern 3pt}QP \subseteq convex{\kern 3pt}QCQP \subseteq SOCP \subseteq SDP )。
Pencils of Semi-Infinite Matrices and Orthogonal Polynomials
Semi-infinite matrices, generalized eigenvalue problems, and orthogonal polynomials are closely related subjects. They connect different domains in mathematics—matrix theory, operator theory, analysis, differential equations, etc.
Semi-Infinite Programming: Theory, Methods, and Applications
2018年10月11日 · Starting from a number of motivating and abundant applications in §2, including control of robots, eigenvalue computations, mechanical stress of materials, and statistical design, the authors describe a class of optimization problems which are referred to as semi-infinite, because their constraints bound functions of a finite number of ...
Definite, Semi-Definite and Indefinite Matrices - Mathonline
Definite, Semi-Definite and Indefinite Matrices. We are about to look at an important type of matrix in multivariable calculus known as Hessian Matrices.
A review of infinite matrices and their applications
2009年2月1日 · Infinite matrices, the forerunner and a main constituent of many branches of classical mathematics (infinite quadratic forms, integral equations, differential equations, etc.) and of the modern operator theory, is revisited to demonstrate its deep influence on the development of many branches of mathematics, classical and modern, replete with ap...
Semi-Infinite Programming, Semidefinite Programming, and …
2024年3月29日 · As mentioned previously (see ), the linear matrix inequality \\(\\sum _{i=1}^m x_iQ_i\\preceq Q_0\\) can be equivalently written as a linear semi-infinite system below: $$\\displaystyle \\begin{aligned}{} \\sum_{i =1}^{m} x_{i}u_{i}(t) \\le u_{0}(t), \\ \\forall t \\in \\left\\{t \\in \\mathbb{R}^{ n}\\colon\\ \\left\\| t\\right\\| =1\\right ...
Algorithms for Square Root of Semi-Infinite Quasi-Toeplitz
2024年4月22日 · A quasi-Toeplitz M-matrix A is an infinite M-matrix that can be written as the sum of a semi-infinite Toeplitz matrix and a correction matrix. This paper is concerned with computing the square root of invertible quasi-Toeplitz M-matrices which preserves the …
Theoretical and computational properties of semi-infinite quasi ...
2022年11月15日 · We have studied properties of semi-infinite M-matrices which belong to the class Q T ∞ of quasi-Toeplitz matrices. We provided sufficient and necessary conditions under which a Q T matrix is an M-matrix.
eigenvalues eigenvectors - Spectrum of semi-infinite Toeplitz …
2020年12月17日 · I am considering a self-adjoint semi-infinite Toeplitz matrix, by which I mean $$M = \left(\begin{array}{ccccc} a_0 & a_1 & a_2 & a_3 & \cdots \\ a_1^*& a_0 & a_1 & a_2 & \ddots \\ a_2^* & a_1^*& a_0 & a_1 & \ddots \\ a_3^*& a_2^* & a_1^*& a_0 & \ddots \\ \vdots & \ddots & \ddots & \ddots & \ddots \end{array}\right) $$ where $\{a_n\}_{n=-\infty ...
Semi-Infinite Quasi-Toeplitz Matrices with Applications to …
2016年11月19日 · We introduce a finite representation of CQT matrices together with algorithms which implement elementary matrix operations. An application to solving quadratic matrix equations of the kind $AX^2+BX+C=0$, encountered in the solution of Quasi-Birth and Death (QBD) stochastic processes with a denumerable set of phases, is presented where $A,B,C ...