Primal-dual entropy-based interior-point algorithms for linear optimization

Karimi, Mehdi; Luo, Shen; Tunçel, Levent

doi:10.1051/ro/2016020

Cited by 4 publications

(1 citation statement)

References 30 publications

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“…30 Another approach is to use interior-point methods that support the quantum relative entropy cone. 17,31,32 Finally, another approach is to use custom first-order splitting methods such as Ref. 33, see also Ref.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Entropy constraints for ground energy optimization

Fawzi,

Scalet

2024

Journal of Mathematical Physics

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We study the use of von Neumann entropy constraints for obtaining lower bounds on the ground energy of quantum many-body systems. Known methods for obtaining certificates on the ground energy typically use consistency of local observables and are expressed as semidefinite programming relaxations. The local marginals defined by such a relaxation do not necessarily satisfy entropy inequalities that follow from the existence of a global state. Here, we propose to add such entropy constraints that lead to tighter convex relaxations for the ground energy problem. We give analytical and numerical results illustrating the advantages of such entropy constraints. We also show limitations of the entropy constraints we construct: they are implied by doubling the number of sites in the relaxation and as a result they can at best lead to a quadratic improvement in terms of the matrix sizes of the variables. We explain the relation to a method for approximating the free energy known as the Markov Entropy Decomposition method.

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Section: Numerical Experimentsmentioning

confidence: 99%

Entropy constraints for ground energy optimization

Fawzi,

Scalet

2024

Journal of Mathematical Physics

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New Predictor–Corrector Algorithm for Symmetric Cone Horizontal Linear Complementarity Problems

Darvay

Rigó

2022

J Optim Theory Appl

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We propose a new predictor–corrector interior-point algorithm for solving Cartesian symmetric cone horizontal linear complementarity problems, which is not based on a usual barrier function. We generalize the predictor–corrector algorithm introduced in Darvay et al. (SIAM J Optim 30:2628–2658, 2020) to horizontal linear complementarity problems on a Cartesian product of symmetric cones. We apply the algebraically equivalent transformation technique proposed by Darvay (Adv Model Optim 5:51–92, 2003), and we use the difference of the identity and the square root function to determine the new search directions. In each iteration, the proposed algorithm performs one predictor and one corrector step. We prove that the predictor–corrector interior-point algorithm has the same complexity bound as the best known interior-point methods for solving these types of problems. Furthermore, we provide a condition related to the proximity and update parameters for which the introduced predictor-corrector algorithm is well defined.

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Interior-point algorithm for symmetric cone horizontal linear complementarity problems based on a new class of algebraically equivalent transformations

Darvay

Rigó

2023

Optim Lett

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We generalize a primal-dual interior-point algorithm (IPA) proposed recently in (Illés T, Rigó PR, Török R Unified approach of primal-dual interior-point algorithms for a new class of AET functions, 2022) to $$P_*(\kappa )$$ P ∗ ( κ ) -horizontal linear complementarity problems (LCPs) over Cartesian product of symmetric cones. The algorithm is based on the algebraic equivalent transformation (AET) technique with a new class of AET functions. The new class is a modification of the class of AET functions proposed in (Illés T, Rigó PR, Török R Unified approach of primal-dual interior-point algorithms for a new class of AET functions, 2022) where only two conditions are used as opposed to three used in (Illés T, Rigó PR, Török R Unified approach of primal-dual interior-point algorithms for a new class of AET functions, 2022). Furthermore, the algorithm is a feasible algorithm that uses full Nesterov-Todd steps, hence, no calculation of step-size is necessary. Nevertheless, we prove that the proposed IPA has the iteration bound that matches the best known iteration bound for IPAs solving these types of problems.

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Primal-dual entropy-based interior-point algorithms for linear optimization

Cited by 4 publications

References 30 publications

Entropy constraints for ground energy optimization

Entropy constraints for ground energy optimization

New Predictor–Corrector Algorithm for Symmetric Cone Horizontal Linear Complementarity Problems

Interior-point algorithm for symmetric cone horizontal linear complementarity problems based on a new class of algebraically equivalent transformations

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