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 )。

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.

Oct 11, 2018 · 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. We are about to look at an important type of matrix in multivariable calculus known as Hessian Matrices.

Feb 1, 2009 · 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...

Mar 29, 2024 · 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 ...

Apr 22, 2024 · 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 quasi-Toeplitz structure.

Nov 15, 2022 · 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.

Dec 17, 2020 · 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 ...

Nov 19, 2016 · 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 ...