An $$O\left(\sqrt{n}L\right)$$ O n L wide neighborhood interior-point algorithm for semidefinite optimization

Pirhaji, Mohammad; Mansouri, Hossein

doi:10.1007/s40314-015-0220-9

Cited by 5 publications

(3 citation statements)

References 23 publications

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“…Their method works in a wide neighborhood of the central path and has the best known theoretical complexity of short-step variants. Based on their approach, several authors proposed long-step methods with the best known theoretical complexity, for different problem classes, e.g., for linear optimization [15,33,41], horizontal linear complementarity problems (HLCPs) [38], symmetric cone Cartesian P * (κ)-HLCPs [4,5], and also for semidefinite optimization [21,32,36].…”

Section: Introductionmentioning

confidence: 99%

A New Ai–Zhang Type Interior Point Algorithm for Sufficient Linear Complementarity Problems

Nagy

Varga

2022

J Optim Theory Appl

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In this paper, we propose a new long-step interior point method for solving sufficient linear complementarity problems. The new algorithm combines two important approaches from the literature: the main ideas of the long-step interior point algorithm introduced by Ai and Zhang and the algebraic equivalent transformation technique proposed by Darvay. Similar to the method of Ai and Zhang, our algorithm also works in a wide neighborhood of the central path and has the best known iteration complexity of short-step variants. However, due to the properties of the applied transforming function in Darvay’s technique, the wide neighborhood definition in the analysis depends on the value of the handicap. We implemented not only the theoretical algorithm but a greedy variant of the new method (working in a neighborhood independent of the handicap) in MATLAB and tested its efficiency on both sufficient and non-sufficient problem instances. In addition to presenting our numerical results, we also make some interesting observations regarding the analysis of Ai–Zhang type methods.

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Section: Introductionmentioning

confidence: 99%

A New Ai–Zhang Type Interior Point Algorithm for Sufficient Linear Complementarity Problems

Nagy

Varga

2022

J Optim Theory Appl

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“…This success is reflected in the large number of recent biomedical, environmental exposure, and soil and ecology studies employing metabolomics approaches. [2][3][4][5][6][7][8][9][10] In contrast to genetic and proteomic information available from rapid genome and proteome sequencing, far less is understood about the totality of human exposure and small molecules found in the environment. [12][13][14] Furthermore, driven by a broader interest in understanding biological impacts of chemical exposures, biomonitoring is undergoing a significant evolution.…”

Section: ■ Introductionmentioning

confidence: 99%

Evaluation of In Silico Multifeature Libraries for Providing Evidence for the Presence of Small Molecules in Synthetic Blinded Samples

Nuñez

Colby

Thomas

et al. 2019

J. Chem. Inf. Model.

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The current gold standard for unambiguous molecular identification in metabolomics analysis is comparing two or more orthogonal properties from the analysis of authentic reference materials (standards) to experimental data acquired in the same laboratory with the same analytical methods. This represents a significant limitation for comprehensive chemical identification of small molecules in complex samples. The process is time consuming and costly, and the majority of molecules are not yet represented by standards. Thus, there is a need to assemble evidence for the presence of small molecules in complex samples through the use of libraries containing calculated chemical properties. To address this need, we developed a Multi-Attribute Matching Engine (MAME) and a library derived in part from our in silico chemical library engine (ISiCLE). Here, we describe an initial evaluation of these methods in a blinded analysis of synthetic chemical mixtures as part of the U.S. Environmental Protection Agency's (EPA) Non-Targeted Analysis Collaborative Trial (ENTACT, Phase 1). For molecules in all mixtures, the initial blinded false negative rate (FNR), false discovery rate (FDR), and accuracy were 57%, 77%, and 91%, respectively. For high evidence scores, the FDR was 35%. After unblinding of the sample compositions, we optimized the scoring parameters to better exploit the available evidence and *

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“…Yang et al [24], based on an important inequality and a new wide neighborhood, suggested a second-order MPC algorithm for SDO problems. Recently, Pirhaji et al [16] proposed a feasible interior-point algorithm for SDO problems in which their algorithm uses the Ai-Zhang wide neighborhood [1] and terminates in at most O ( √ nL) iterations.…”

Section: Introductionmentioning

confidence: 99%

A Mehrotra predictor-corrector interior-point algorithm for semidefinite optimization

Pirhaji¹,

Mansouri²

2017

Turk J Math

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This paper proposes a second-order Mehrotra-type predictor-corrector feasible interior-point algorithm for semidefinite optimization problems. In each iteration, the algorithm computes the Newton search directions through a new form of combination of the predictor and corrector directions. Using the Ai-Zhang wide neighborhood for linear complementarity problems, it is shown that the complexity bound of the algorithm is O (√ n log ε −1 ) for the Nesterov-Todd search direction and O ( n log ε −1 ) for the Helmberg-Kojima-Monteiro search directions.

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An $$O\left(\sqrt{n}L\right)$$ O n L wide neighborhood interior-point algorithm for semidefinite optimization

Cited by 5 publications

References 23 publications

A New Ai–Zhang Type Interior Point Algorithm for Sufficient Linear Complementarity Problems

A New Ai–Zhang Type Interior Point Algorithm for Sufficient Linear Complementarity Problems

Evaluation of In Silico Multifeature Libraries for Providing Evidence for the Presence of Small Molecules in Synthetic Blinded Samples

A Mehrotra predictor-corrector interior-point algorithm for semidefinite optimization

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