## Mathematical programming and control theory

B.D. Craven

[目次]

• 1 Optimization problems
• introduction.- 1.1 Introduction.- 1.2 Transportation network.- 1.3 Production allocation model.- 1.4 Decentralized resource allocation.- 1.5 An inventory model.- 1.6 Control of a rocket.- 1.7 Mathematical formulation.- 1.8 Symbols and conventions.- 1.9 Differentiability.- 1.10 Abstract version of an optimal control problem.- References.- 2 Mathematical techniques.- 2.1 Convex geometry.- 2.2 Convex cones and separation theorems.- 2.3 Critical points.- 2.4 Convex functions.- 2.5 Alternative theorems.- 2.6 Local solvability and linearization.- References.- 3 Linear systems.- 3.1 Linear systems.- 3.2 Lagrangean and duality theory.- 3.3 The simplex method.- 3.4 Some extensions of the simplex method.- References.- 4 Lagrangean theory.- 4.1 Lagrangean theory and duality.- 4.2 Convex nondifferentiable problems.- 4.3 Some applications of convex duality theory.- 4.4 Differentiable problems.- 4.5 Sufficient Lagrangean conditions.- 4.6 Some applications of differentiable Lagrangean theory.- 4.7 Duality for differentiable problems.- 4.8 Converse duality.- References.- 5 Pontryagin theory.- 5.1 Introduction.- 5.2 Abstract Hamiltonian theory.- 5.3 Pointwise theorems.- 5.4 Problems with variable endpoint.- References.- 6 Fractional and complex programming.- 6.1 Fractional programming.- 6.2 Linear fractional programming.- 6.3 Nonlinear fractional programming.- 6.4 Algorithms for fractional programming.- 6.5 Optimization in complex spaces.- 6.6 Symmetric duality.- References.- 7 Some algorithms for nonlinear optimization.- 7.1 Introduction.- 7.2 Unconstrained minimization.- 7.3 Sequential unconstrained minimization.- 7.4 Feasible direction and projection methods.- 7.5 Lagrangean methods.- 7.6 Quadratic programming by Beale's method.- 7.7 Decomposition.- References.- Appendices.- A.1 Local solvability.- A.2 On separation and Farkas theorems.- A.3 A zero as a differentiable function.- A.4 Lagrangean conditions when the cone has empty interior.- A.5 On measurable functions.- A.6 Lagrangean theory with weaker derivatives.- A.7 On convex functions.

「Nielsen BookData」より

書名 Mathematical programming and control theory Craven, B. D. Craven B.D. Chapman and Hall mathematics series Chapman and Hall Distributed in the U.S.A. by Halsted Press Wiley 1978 xi, 163 p. 23 cm 0412155001 0470264071 0470264136 0412154900 BA03492357 ※クリックでCiNii Booksを表示 英語 イギリス
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