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illustrate how the function c k concatenates the constant functions at the ends of interval [0, 1] to make the piese-wise polynomial function as smooth as possible.
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![Fig. 1: Comparison of c 0 (t) and c 4 (t) over [0, 1] in terms of their...](publication/381517639/figure/fig2/AS:11431281252602994@1718766919501/Comparison-of-c-0-t-and-c-4-t-over-0-1-in-terms-of-their-smoothness-at-the-end_Q320.jpg)
We introduce a S.O.S hierarchy of lower bounds for a polynomial optimization problem whose constraint is expressed as a matrix polynomial semidefinite condition. Our approach involves utilizing a penalty function framework to directly address the matrix-based constraint, making it applicable to both discrete and continuous polynomial optimization p...
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