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Conten&
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18.9 Inequality constraints: Kuhn-Tucker conditions
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18.9.1
Second-order conditions for inequality constraints
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18.9.2
An extension: Fritz John conditions
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1
8.10 Exercises
18.11 References
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19
Shortest-Path Algorithms and Dynamic Programming
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19.1 Definitions for graphs
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19.2 Dynamic programming
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19.3 The Viterbi algorithm
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19.4
Code for the Viterbi algorithm
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19.4.1
Related algorithms: Dijkstra's and Warshall's
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19.4.2
Complexity comparisons of Viterbi and Dijkstra
Applications of path search algorithms
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19.5 Maximum-likelihood sequence estimation
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19.5.1
The intersymbol interference
(ISI)
channel
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19.5.2 Code-division multiple access
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19.5.3 Convolutional decoding
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19.6
HMM likelihood analysis and HMM training
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19.6.1 Dynamic warping
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19.7 Alternatives to shortest-path algorithms
19.8 Exercises
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19.9 References
20
Linear Programming
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20.1 Introduction to linear programming
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20.2
Putting a problem into standard form
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20.2.1
Inequality constraints and slack variables
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20.2.2 Free variables
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20.2.3 Variable-bound constraints
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20.2.4
Absolute value in the objective
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20.3
Simple examples of linear programming
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20.4
Computation of the linear programming solution
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20.4.1 Basic variables
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20.4.2 Pivoting
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20.4.3 Selecting variables on which to pivot
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20.4.4 The effect of pivoting on the value of the problem
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20.4.5 Summary of the simplex algorithm
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20.4.6 Finding the initial basic feasible solution
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20.4.7
MATLAB@
code for linear programming
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20.4.8 Matrix notation for the silnplex algorithm
20.5 Dual problems
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20.6 Karmarker's algorithm for LP
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20.6.1 Conversion to Karmarker standard form
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20.6.2 Convergence of the algorithm
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20.6.3 Su~nrnary and extensions
Examples and applications of linear programming
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20.7 Linear-phase
FIR
filter design
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20.7.1 Least-absolute-error approximation
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20.8 Linear optimal control