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Dennis J.B. Ч Mathematical Programming and Electrical Networks
Dennis J.B. Ч Mathematical Programming and Electrical Networks

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Ќазвание: Mathematical Programming and Electrical Networks

јвтор: Dennis J.B.

јннотаци€:

Solving certain mathematical programming problems by setting up an equivalent electrical network which automatically establishes a current distribution that represents an optimal solution.


язык: en

–убрика: “ехнологи€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 1 edition

√од издани€: 1959

 оличество страниц: 186

ƒобавлена в каталог: 28.03.2010

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Algorithms for diode-source networks      56Ч71
Algorithms for linear programming      101Ч107
Algorithms for network flow problems      73Ч74
Algorithms for quadratic programming      104Ч107
Algorithms for the maximum flow problem      72Ч73
Algorithms for the shortest path problem      71Ч72
Basic solution of generalized terminal-pair system      171
Basic solution of terminal-pair system      81
Breakpoint curves as solution set of a terminal-pair system      159Ч168
Breakpoint curves as terminal characteristic of networks containing diodes      39Ч43
Breakpoint curves, defined      159Ч160
Breakpoint tracing method for a reduced terminal-pair system      91Ч92
Breakpoint tracing method for a terminal-pair system      82Ч87
Breakpoint tracing method for an uncoupled system      88Ч91
Breakpoint tracing method for the completely degenerate system      92
Breakpoint tracing method for the generalized system      87Ч88 169Ч180
By-pass method for linear and quadratic programming      103Ч106
By-pass method for obtaining feasibility      98Ч101
Complemementary slackness and the diode circuit element      34
Complemementary slackness in general programming      12Ч17
Complemementary slackness principle, for concave programming      157
Complemementary slackness principle, for linear and quadratic programming      25 143Ч144
Concave (convex) functions      9Ч11 148Ч152
Concave (convex) functions, defined      148
Concave (convex) functions, properties      148Ч152
Concave (convex) programming      26 38Ч39 153Ч158
Concave (convex) programming and nonlinear resistors      38Ч39
Concave (convex) programming, complementary slackness      157
Concave (convex) programming, duality      26 157
Concave (convex) programming, Lagrangian problem      154
Cone, defined      12
Conjugate variable pairs      81
Constraint qualifications      132Ч133 135Ч137
Constraint set      7
Convex hull, defined      120
Convex set, defined      120
Convex set, defined by convex inequalities      10 131
Convex set, polyhedral      121
Current reduced network      34Ч35 56 93 96Ч101
Current source      29
Degeneracy in the breakpoint tracing method      81 87 169
Diode and complementary slackness      34
Diode, defined      29Ч31
Diode-source networks, algorithms for solving      56Ч71
Diode-source networks, existence conditions      54Ч55
Diode-source networks, nonredundancy assumptions      53Ч54
Duality and conservation of energy      34 93
Duality in ordinary minimization      21Ч23
Duality theorem, for concave programming      157
Duality theorem, for linear and quadratic programming      23Ч25 141
Duality, topological, for diode-source networks      51
Electrical devices, current sources      29
Electrical devices, diodes      29Ч31
Electrical devices, resistors, linear      31
Electrical devices, resistors, nonlinear      38Ч39
Electrical devices, transformers      31
Electrical devices, voltage sources      29
Electrical models for linear programming      93Ч95
Electrical models for maximum flow problem      47Ч48
Electrical models for network flow problem      51Ч52
Electrical models for quadratic programming      93Ч95
Electrical models for shortest path problem      49Ч51
Electrical models for terminal-pair system      78Ч80
Electrical networks, diode-source      53Ч71
Electrical networks, diode-source-resistor      31Ч34
Electrical networks, graphs      27
Electrical networks, incidence matrix      27Ч28
Electrical networks, laws      29
Electrical networks, reduced      34Ч35 56Ч62 67Ч68 93 96Ч101
Electrical networks, with ideal transformers      35Ч37
Existence conditions for diode-source networks      54Ч56
Existence theorem for linear and quadratic programming      142
Existence theorem, interpretation in terms of reduced networks      34Ч35
Extreme point, defined      120
Feasible vector      6
Ford Ч Fulkerson method      73Ч74
Functions, concave (convex)      9Ч11 148
Functions, Legendre transformation      18Ч21 148Ч152
Functions, strict increase property      148
General programming problem      6Ч7 9Ч17 113Ч117 131Ч137
General programming problem, complementary slackness      12Ч17
General programming problem, constraint qualification      132Ч133 135Ч137
General programming problem, fundamental theorem      17 133Ч134
General programming problem, Kuhn Ч Tucker conditions      12Ч17 133Ч134
General programming problem, Lagrange multipliers      11Ч17
General programming problem, Lagrangian problem      11Ч17 133
General programming problem, local and global minima      9Ч11 131Ч132
General programming problem, method of steepest descent for      113Ч117
Generalized terminal-pair system      87Ч88 169Ч180
Gradient method for equality constrained minimization      110Ч113
Gradient method for the general programming problem      113Ч117
Gradient method for unconstrained minimization      109Ч110
Graph of a network      27Ч28
Half space, defined      119
Hyperplane, defined      119
Incidence matrix      27Ч28
Incremental solutions of terminal pair system      82Ч83
KirchoffТs loop law      29
KirchoffТs node law      29
Kuhn Ч Tucker conditions      12Ч17 133Ч134
Lagrange multipliers      11Ч17
Lagrangian problem for concave programming      154
Lagrangian problem for equality constrained minimization      22
Lagrangian problem for linear and quadratic programming      24 139Ч149
Lagrangian problem for the general programming problem      11Ч17
Legendre transformation      18Ч21 148Ч152
Legendre transformation, defined      20 152
Legendre transformation, example      21
Legendre transformation, properties      148Ч152
Line, defined      12
Linear programming      7Ч8 23Ч25 93Ч95 101Ч107 138Ч147
Linear programming, by-pass algorithm      104Ч107
Linear programming, complementary slackness      25 143Ч144
Linear programming, duality      23Ч25 141
Linear programming, electrical model      93Ч95
Linear programming, existence of optima      25 141
Linear programming, valve algorithm      101Ч103
Local minima      9Ч10 109 131
Loop, in a network      53
Maximum flow problem, algorithm for      72Ч73
Maximum flow problem, electrical model      47Ч48
Minimization problems, duality in      21Ч23
Minimization problems, equality constrained, steepest descent method      110Ч113
Minimization problems, quadratic      21Ч23
Minimization problems, steepest descent method for      108Ч110
Monotone functions, strict increase property      148
Network flow problems      45Ч53 71Ч75
Network flow problems with quadratic costs      74Ч75
Network flow problems, electrical model      51Ч52
Network flow problems, Ford Ч Fulkerson algorithm      73Ч74
Notation      4Ч5
Objective function      6
Optimal vector      7
Path, in a network      53
Power      29
Power and duality      34 93
Primal-dual method      106
Programming, concave (convex)      26 38Ч39 153Ч158
Programming, general (nonlinear)      6Ч7 9Ч17 113Ч117 131Ч137
Programming, linear      7Ч8 23Ч25 93Ч95 101Ч107 138Ч147
Programming, quadratic      8 23Ч26 93Ч95 104Ч107 138Ч147
Quadratic programming      8 23Ч26 93Ч95 104Ч107 138Ч147
Quadratic programming, application to a steepest descent method for the general programming problem      114Ч117
Quadratic programming, by-pass algorithm      104Ч107
Quadratic programming, complementary slackness      25 143Ч144
Quadratic programming, duality      23Ч25 141
Quadratic programming, electrical models      93Ч95
Quadratic programming, existence of solutions      25 142
Quadratic programming, Lagrangian problem      24
Quadratic programming, uniqueness      24 143Ч144
Reduced networks and existence of solutions      35 54Ч56
Reduced networks and feasibility      34Ч35 93
Reduced networks, current      34Ч35 56 67Ч68 93 96Ч101
Reduced networks, voltage      34Ч35 56Ч62 93 101
Relative minima      9Ч11 109 131
Shortest path problem, algorithm for      71Ч72
Shortest path problem, electrical model      49Ч51
Simplex method      77Ч78 103
Steepest descent method for equality constrained minimization      110Ч113
Steepest descent method for nonlinear programming      113Ч117
Steepest descent method for unconstrained minimization      108Ч110
Strict increase property      148
Summary of results      2Ч3
Terminal pair system for linear programming      101Ч107
Terminal pair system for obtaining feasibility      96Ч101
Terminal pair system for quadratic programming      104Ч107
Terminal pair system, basic solutions      81
Terminal pair system, completely degenerate      92
Terminal pair system, degeneracy      81 87 169
Terminal pair system, dual reduced      92
Terminal pair system, electrical model for      78Ч79
Terminal pair system, generalized      87Ч88 169Ч180
Terminal pair system, incremental solutions      82Ч83
Terminal pair system, primal reduced      91Ч92
Terminal pair system, terminal solutions and break-point curves      39Ч43
Terminal pair system, tracing procedure      82Ч87
Terminal pair system, uncoupled      88
Terminal pair system, unit solutions      82Ч83
Transportation problem      46
Uniqueness of solutions in concave programming      157
Uniqueness of solutions in quadratic programming      25 143Ч144
Unit solutions of terminal-pair system      82Ч83
Valve algorithm for linear programming      101Ч103
Valve algorithm for obtaining feasibility      96Ч98 101
Voltage reduced network      34Ч35 56Ч62 93 101
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