Linear programming with matrix variables
B. D. Craven,Bertram Mond +1 more
17
TL;DR: The duality theorems for linear programming over complex spaces, and over quaternion spaces, follow as special cases as discussed by the authors, with the inner product defined using trace of a matrix.
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About: This article is published in Linear Algebra and its Applications. The article was published on 01 Jun 1981. and is currently open access. The article focuses on the topics: Coefficient matrix & Theorems and definitions in linear algebra.
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Citations
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Linear Matrix Inequalities in System and Control Theory
Edwin E. Yaz
- 01 Jan 1994
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
Semidefinite programming
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Handbook of Semidefinite Programming
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- 01 Jan 2000
TL;DR: Conditions and an accurate semidefinite programming solver are described in The Journal of the SDPA family for solving large-scale SDPs and in Handbook on Semidefinitely Programming.
On Eigenvalue Optimization
TL;DR: A general framework for a smooth (differentiable) approach to optimization problems involving eigenvalues of symmetric matrices is presented, based on the concept of transversality borrowed from differential geometry.
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References
•Book
Mathematical programming and control theory
B. D. Craven
- 01 Jan 1978
TL;DR: In this article, Lagrangean and duality theory was used to solve the problem of optimal control problems in the context of convex non-differentiable problems and differentiable problems.
188
Lagrangean conditions and quasiduality
TL;DR: In this article, the Lagrangean necessary conditions for a minimum are well known, but are subject to certain hypotheses concerning cones, which are now substantially weakened, but a counter example shows that they cannot be omitted altogether.
112
On Systems of Linear Inequalities in Hermitian Matrix Variables
Richard Ernest Bellman,Ky Fan +1 more
- 01 Jan 1962
76