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In convex optimization, a linear matrix inequality (LMI) is an expression of the form ():= + + + + where = [, =, …,] is a real vector,,,, …, are symmetric matrices, is a generalized inequality meaning is a positive semidefinite matrix belonging to the positive semidefinite cone + in the subspace of symmetric matrices .
Download as PDF; Printable version ... Bendixson's inequality; Weyl's inequality in matrix theory; ... a bound on the largest absolute value of a linear combination ...
Finsler's lemma can be used to give novel linear matrix inequality (LMI) characterizations to stability and control problems. [4] The set of LMIs stemmed from this procedure yields less conservative results when applied to control problems where the system matrices has dependence on a parameter, such as robust control problems and control of ...
In mathematics, Farkas' lemma is a solvability theorem for a finite system of linear inequalities. It was originally proven by the Hungarian mathematician Gyula Farkas . [ 1 ] Farkas' lemma is the key result underpinning the linear programming duality and has played a central role in the development of mathematical optimization (alternatively ...
In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: [1] < less than > greater than; ≤ less than or equal to; ≥ greater than or equal to; ≠ not equal to; A linear inequality looks exactly like a linear equation, with the inequality sign ...
Download as PDF; Printable version ... In linear algebra, Weyl's inequality is a theorem about the changes to eigenvalues of an Hermitian matrix that is perturbed. It ...
Let denote the space of Hermitian matrices, + denote the set consisting of positive semi-definite Hermitian matrices and + + denote the set of positive definite Hermitian matrices. For operators on an infinite dimensional Hilbert space we require that they be trace class and self-adjoint , in which case similar definitions apply, but we discuss ...
More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope , which is a set defined as the intersection of finitely many half spaces , each of which is defined by a linear inequality.
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