Convex optimization transform

  • 1.
    1. Convex Models A convex model is defined mathematically as a set of functions.
    2. Each function is a realization of an uncertain event.
      Several interesting. (1996), Pantelides and Tzan (1996), Tzan and Pantelides (1996a) and Baratta et al.
Any convex optimization problem can thus be reformulated in the form of an equivalent convex problem with linear objective. In certain cases, we can substitute an equality constraint of the form b(x) = u with an inequality constraint b(x) ≤ u.
Wikipedia claims that: Any convex optimization problem can be transformed into minimizing (or maximizing) a linear function over a convex set by converting to the epigraph form.

N-th power Fourier transform

In mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform.
It can be thought of as the Fourier transform to the n-th power, where n need not be an integer — thus, it can transform a function to any intermediate domain between time and frequency.
Its applications range from filter design and signal analysis to phase retrieval and pattern recognition.

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