2019
DOI: 10.48550/arxiv.1909.07263
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An algorithm based on continuation techniques for minimization problems with highly non-linear equality constraints

Abstract: We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local minimization algorithms with random starting guesses. We are particularly interested in the computation of minimal norm solutions of underdetermined systems of polynomial equations. Such systems arise, for instance, in the context of the construction of high order optimized di… Show more

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Cited by 1 publication
(4 citation statements)
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“…This solution is then taken as the starting point of an arc-length continuation method and follow the solution along the curve leading to a local minimum of the 1-norm of the vector of coefficients. In doing so we apply the algorithm presented in [1,2]. After this process, we check several methods in practice and finally the solution A 18 collected in Table 4, with E f , ∆ and δ given in Table 3.…”
Section: New Methods Of Ordermentioning
confidence: 99%
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“…This solution is then taken as the starting point of an arc-length continuation method and follow the solution along the curve leading to a local minimum of the 1-norm of the vector of coefficients. In doing so we apply the algorithm presented in [1,2]. After this process, we check several methods in practice and finally the solution A 18 collected in Table 4, with E f , ∆ and δ given in Table 3.…”
Section: New Methods Of Ordermentioning
confidence: 99%
“…This is called the number of stages of the method. Notice that, if the Strang splitting is used as the scheme S [2] h in the composition (1.8), the number of stages is also m. From Table 1 it is then straightforward to estimate the minimum number of stages to achieve an even order r = 2k. For the composition (1.8) and the general splitting (1.5) these values are, respectively,…”
Section: Order Conditionsmentioning
confidence: 99%
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