Nonlinear Programming Peter Zörnig ISBN: 978-3-11-031527-1 © 2014 by Walter de Gruyter GmbH, Berlin/Boston Abbildungsübersicht / List of Figures Tabellenübersicht.

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Presentation transcript:

Nonlinear Programming Peter Zörnig ISBN: © 2014 by Walter de Gruyter GmbH, Berlin/Boston Abbildungsübersicht / List of Figures Tabellenübersicht / List of Tables

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston Fig Graphical illustration of the transportation problem. 2

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 3 Table 1.1. Data of the meteorological observatory.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 4 Fig Dispersion diagram.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 5 Fig Measurements of a box.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 6 Fig Measures of the modified box.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 7 Fig Locations of gas stations and demands.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 8 Table 1.2. Heights of terrain and road.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 9 Fig Terrain and optimal road height.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 10 Fig Nonconvex feasible region.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 11 Fig Nonconnected feasible region.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 12 Fig Optimal point in the interior of M.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 13 Fig Local and global minimum points.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 14 Fig Feasible and nonfeasible directions.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 15 Fig Cone Z(x ∗ ) of Example 2.2 (a).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 16 Fig Cone Z(x ∗ ) of Example 2.2 (b).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 17 Fig Cone of feasible directions for linear constraints.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 18 Fig Cone of feasible directions with L 0 (x ∗ ) ≠ Z(x ∗ ) ≠ L(x ∗ ).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 19 Fig Geometric illustration of Example 2.11.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 20 Fig Line segment [x 1, x 2 ].

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 21 Fig Convex and nonconvex sets.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 22 Fig Convex polyhedral sets.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 23 Fig Extreme points of convex sets.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 24 Fig Convex hull of a finite set.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 25 Fig Convex hulls of nonfinite sets.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 26 Fig Simplex of dimension 2 and 3.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 27 Fig Illustration of Theorem 3.12.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 28 Fig Convex and concave functions.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 29 Fig Illustration of Theorem 3.25.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 30 Fig The epigraph of a function.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 31 Fig Supporting hyperplanes of convex sets.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 32 Fig Support function of f at x ∗.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 33 Fig Support functions of the function f of Example 3.35.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 34 Fig The function f (x1, x2) = |x1| + |x2|.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 35 Fig Illustration of Theorem 3.48.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 36 Fig Minimum point of a concave function.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 37 Fig Nonregular point x ∗ = 0.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 38 Fig Illustration of the Farkas lemma.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 39 Fig Geometrical illustration of KKT conditions.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 40 Fig Illustration of the relation (4.22).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 41 Fig Illustration of Example 4.8.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 42 Fig Illustration of Example 4.14.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 43 Fig Saddle point.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 44 Fig Geometric illustration of (P).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 45 Fig Geometric illustration of (D).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 46 Fig Function h 1 (x 1 ) for various values of u.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 47 Fig Dual objective function.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 48 Fig Geometrical solution of Example 4.47 (case a).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 49 Fig Geometrical solution of Example 4.47 (case b).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 50 Fig Illustration of Example 4.50.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 51 Fig Unimodal function.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 52 Fig Locating of x.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 53 Fig Construction of the new interval [a k+1, b k+1 ].

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 54 Table 6.1. Golden Section.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 55 Fig Iteration of Newton’s method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 56 Fig Construction of a useless value.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 57 Fig Cycling of Newton’s method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 58 Fig Interpolation polynomials of Example 6.17.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 59 Fig Interpolation polynomials of Example 6.20.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 60 Fig Orthogonal coordinate transformations.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 61 Fig Level curves of the function 2x x 1 x 2 + 5x 2 2.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 62 Fig Level surface z = 6 for the function 7x 2 1 − 2x 1 x 2 + 4x 1 x 3 + 7x 2 2 − 4x 2 x x 2 3.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 63 Table 7.1. Gradient method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 64 Fig Minimization process of the gradient method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 65 Table 7.2. Conjugate gradient method (quadratic problem).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 66 Table 7.3. Conjugate gradient method (nonquadratic problem).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 67 Fig Solution of Example 7.30 by the conjugate gradient method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 68 Table 7.4. DFP method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 69 Table 7.5. Cyclic minimization.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 70 Fig Solution of Example 7.38.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 71 Table 7.6. Inexact line search (case a).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 72 Fig Convergence to a nonoptimal point.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 73 Table 7.7. Inexact line search (case b).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 74 Fig Oscillation of the algorithm.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 75 Fig Reversal strategy.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 76 Fig Solution of the quadratic subproblem.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 77 Fig Trust region method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 78 Fig Construction of the search direction.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 79 Fig Resolution of Example 8.2 by Rosen’s method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 80 Fig Optimal directions.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 81 Fig Zigzag movement.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 82 Table 8.1. Pivoting of Example 8.17.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 83 Fig Active set method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 84 Table 9.1. Initial tableau of Lemke’s method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 85 Table 9.2. Pivot steps of Example 9.4.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 86 Table 9.3. Pivot steps of Example 9.5.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 87 Fig Unbounded optimal solution.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 88 Fig Locations of gas stations.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 89 Fig Penalty terms.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 90 Fig Function q(x, r) of Example 10.2.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 91 Fig Function q(x, r) of Example 10.2.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 92 Fig Penalty method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 93 Fig Exact penalty function (10.12).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 94 Fig Illustration of robustness.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 95 Fig Barrier terms.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 96 Fig Barrier function s(x, c) of Example

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 97 Table Solution of Example

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 98 Table Solution of Example

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 99 Fig Barrier method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 100 Fig Partial cost function.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 101 Fig Nondifferentiable function of a minimax problem.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 102 Fig Nondifferentiable bidimensional objective function.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 103 Fig Graphical solution of problem (11.9).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 104 Fig Objective function of problem (11.8).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 105 Fig Minimization of function (11.10) with the gradient method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 106 Fig Minimization of function (11.11) with the gradient method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 107 Fig Piecewise linear function f and differential approximation g for ε = 0.1.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 108 Table Minimization by differentiable approximation.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 109 Fig Local and global minima of problem (11.28).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 110 Fig D.c. function.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 111 Fig Branch-and-bound method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 112 Fig Branch-and-bound method (continuation).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 113 Fig Subdivisions of the feasible region.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 114 Fig Optimization problem (11.36).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 115 Table Population P(0).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 116 Table Population P(1).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 117 Fig Feasible set and gradients.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 118 Fig Feasible region and gradients.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 119 Fig Feasible directions at x ∗ in diverse cases.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 120 Fig Algebraic sum.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 121 Fig Feasible direction.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 122 Fig Discontinuous concave function.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 123 Fig Convex function.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 124 Fig Geometrical illustration of the subdifferential.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 125 Fig Dispersion diagram.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 126 Fig Feasible region.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 127 Fig Regular point x ∗ = 0 with linearly dependent gradients.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 128 Fig Geometric resolution of Exercise 4.9.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 129 Fig Geometric solution of Exercise 4.15.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 130 Fig Geometric solution of Exercise 4.33.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 131 Fig Geometric solution of Exercise 4.34.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 132 Table 5.1. Error sequence.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 133 Table 5.2. Linear and quadratic convergence.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 134 Table 6.2. Golden Section.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 135 Table 6.3. Bisection algorithm.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 136 Fig Premature convergence of the bisection method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 137 Fig Hermite interpolation polynomial.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 138 Fig Level curves of Exercise 7.7.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 139 Fig Displaced ellipses.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 140 Fig Level curves of quadratic functions.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 141 Table 7.8. Gradient method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 142 Table 7.9. Newton’s method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 143 Fig Minimization process of Newton’s method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 144 Table Conjugate gradient method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 145 Table DFP method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 146 Table Conjugate gradient method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 147 Table DFP method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 148 Table Variant of the DFP method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 149 Table Cyclic minimization.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 150 Fig Level curves of the first quadratic model of Example 7.50.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 151 Fig Level curves of the function of Exercise 7.54 (b).

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 152 Fig Geometric solution of Exercise 8.7.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 153 Fig Feasible region.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 154 Fig Zoutendijk’s method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 155 Fig Graphical illustration of both methods.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 156 Table 8.2. Pivoting of Example 8.18.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 157 Table 9.4. Lemke’s method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 158 Table 9.5. Lemke’s method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 159 Table Barrier method.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 160 Fig Solution process.

Nonlinear Programming, Peter Zörnig ISBN © 2014 by Walter de Gruyter GmbH, Berlin/Boston 161 Table Barrier method.