By John R. Pierce
Covers encoding and binary digits, entropy, language and which means, effective encoding and the noisy channel, and explores ways that details concept pertains to physics, cybernetics, psychology, and artwork. "Uncommonly good...the such a lot pleasing dialogue to be found." - medical American. 1980 version.
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Extra info for An Introduction to Information Theory: Symbols, Signals and Noise
2) at the center point w0 of X0 , split the hyper-rectangle X0 by a hyperplane through w0 and orthogonal to an arbitrary axis. 3 has no solution . 3 (handling infeasibility). 3 is infeasible, split the hyper-rectangle X0 by a hyperplane through its center and orthogonal to an arbitrary axis. 1 Multi-parametric Nonlinear Programming 23 5. Algorithm for explicit approximate solution of non-convex mp-NLPs. Assume the tolerance ε¯ > 0 of the objective function approximation error is given. e. n SX0 = ∏ Δ xi , where Δ xi is the size of X0 along the variable xi .
A similar approach was taken in , using a simplex partition instead of hyperrectangles, and in  that exploits the Delaunay tessellation. A reformulation of the MPC problem solving a sequence of simpler explicit MPC problems of horizon N = 1 and a nested sequence of terminal sets, a la dynamic programming, was proposed in . Another sub-optimal approach based on short horizons was proposed in . The use of nested invariant sets and interpolation techniques is pursued for approximations in .
2) only for the discrete set of points W0 ⊂ X0 . 50) for the region X0 , the already computed solutions of this problem in some of the neighboring regions can be used as initial guesses. 3. Estimation of error bounds. 3. Then it follows that the sub-optimal objective function V (x) = f (z0 (x), x) is an approximate upper bound on V ∗ (x) in X0 , such that for all x ∈ X0 , where z0 (x) is feasible, we have: 0 ≤ V (x) − V ∗ (x) ≤ ε0 . 1 Multi-parametric Nonlinear Programming 21 As already mentioned, the objective function f can be non-convex with multiple local minima.