We present a polynomial-time primal-dual interior-point algorithm (IPA) for solving convex quadratic optimization (CQO) problems, based on a bi-parameterized bi-hyperbolic kernel function (KF). The growth term is a co...
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We present a polynomial-time primal-dual interior-point algorithm (IPA) for solving convex quadratic optimization (CQO) problems, based on a bi-parameterized bi-hyperbolic kernel function (KF). The growth term is a combination of the classical quadratic term and a hyperbolic one depending on a parameter p is an element of [0, 1], while the barrier term is hyperbolic and depends on a parameter q >= 1/2 sinh 2. Using some simple analysis tools, we prove with a special choice of the parameter q, that the worst-case iteration bound for the new corresponding algorithm is O(root n log n log n/epsilon) iterations for large-update methods. This improves the result obtained in (Optimization 70 (8), 1703-1724 (2021)) for CQO problems and matches the currently best-known iteration bound for large-update primal-dual interior-point methods (IPMs). Numerical tests show that the parameter p influences also the computational behavior of the algorithm although the theoretical iteration bound does not depends on this parameter. To our knowledge, this is the first bi-parameterized bi-hyperbolic KF-based IPM introduced for CQO problems, and the first KF that incorporates a hyperbolicfunction in its growth term while all KFs existing in the literature have a polynomial growth term exepct the KFs proposed in (Optimization 67 (10), 1605-1630 (2018)) and (J. Optim. Theory Appl. 178, 935-949 (2018)) which have a trigonometric growth term.
In this paper,we introduce for the first time a new eligible kernelfunction with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel *** prove ...
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In this paper,we introduce for the first time a new eligible kernelfunction with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel *** prove that the interior-point algorithm based on the new kernelfunction meets O(n3/4 logε/n)iterations as the worst case complexity bound for the large-update *** coincides with the complexity bound obtained by the first kernelfunction with a trigonometric barrier term proposed by El Ghami et ***2012,and improves with a factor n(1/4)the obtained iteration bound based on the classic kernel *** present some numerical simulations which show the effectiveness of the algorithm developed in this paper.
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