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Sparse Polynomial Optimization
2022The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of finite-dimensional convex problems. At each step of the associated hierarchy, one needs to solve a fixed size semidefinite program,
Magron, Victor, Wang, Jie
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Journal of Graphics Tools, 2005
In this paper, we present a family of circular or square optimal polynomial filters for prefiltering two-dimensional polygons and images.
Zhouchen Lin +3 more
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In this paper, we present a family of circular or square optimal polynomial filters for prefiltering two-dimensional polygons and images.
Zhouchen Lin +3 more
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Optimization of Polynomial Functions
Canadian Mathematical Bulletin, 2003AbstractThis paper develops a refinement of Lasserre's algorithm for optimizing a polynomial on a basic closed semialgebraic set via semidefinite programming and addresses an open question concerning the duality gap. It is shown that, under certain natural stability assumptions, the problem of optimization on a basic closed set reduces to the compact ...
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Optimization of Polynomial Fractional Functions
Journal of Global Optimization, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tuy, Hoang +2 more
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Computing, 1972
Stability Polynomials characterize the propagation behaviour of the error vectors associated with the numerical solution of differential equations. It is desirable that these polynomials extend as far as possible along the negativex-axis in a strip of width 2.
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Stability Polynomials characterize the propagation behaviour of the error vectors associated with the numerical solution of differential equations. It is desirable that these polynomials extend as far as possible along the negativex-axis in a strip of width 2.
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Optimal reparameterization of polynomial algebraic curves
ACM SIGSAM Bulletin, 1999In this paper, we present an algorithm for optimally parametrizing polynomial algebraic curves. Let [Formula: see text] be a polynomial plane algebraic curve given by a polynomial parametrization [Formula: see text] , where [Formula: see text] is a finite field extension of a field [Formula: see text] of characteristic zero.
Sendra, J. Rafael, Villarino, Carlos
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Polynomial optimization problems
USSR Computational Mathematics and Mathematical Physics, 1987A method for locating global extrema in polynomial optimization problems is proposed. The idea of the method is to reduce the problem to a finite sequence of problems that involve finding the location of the real roots of algebraic polynomials.
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Quadrature-based polynomial optimization
Optimization Letters, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Martinez, Angeles +3 more
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Optimal segmented polynomial L s -approximations
Computing, 1981Characteristic properties of such approximations are given. An algorithm providing good, but not necessarily best, approximations is also discussed.
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Generalized Polynomial Optimization
SIAM Journal on Applied Mathematics, 1967Passy, U., Wilde, D. J.
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