Alternating direction method of multipliers as a simple effective heuristic for mixed-integer nonlinear optimization

Kanno, Yoshihiro; Kitayama, Satoshi

doi:10.1007/s00158-018-1946-y

Cited by 15 publications

(4 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In future work, we will try to use multiple restarts of ADMM with random initial points, which can be regarded as a heuristic algorithm, to approximate the non-convex problem in Eq (19) [70]. Furthermore, the effectiveness of evolutionary algorithm for optimizing our approach will also be tested.…”

Section: Discussionmentioning

confidence: 99%

Low-rank graph optimization for multi-view dimensionality reduction

et al. 2019

View full text Add to dashboard Cite

Graph-based dimensionality reduction methods have attracted substantial attention due to their successful applications in many tasks, including classification and clustering. However, most classical graph-based dimensionality reduction approaches are only applied to data from one view. Hence, combining information from different data views has attracted considerable attention in the literature. Although various multi-view graph-based dimensionality reduction algorithms have been proposed, the graph construction strategies utilized in them do not adequately take noise and different importance of multiple views into account, which may degrade their performance. In this paper, we propose a novel algorithm, namely, Low-Rank Graph Optimization for Multi-View Dimensionality Reduction (LRGO-MVDR), that overcomes these limitations. First, we construct a low-rank shared matrix and a sparse error matrix from the graph that corresponds to each view for capturing potential noise. Second, an adaptive nonnegative weight vector is learned to explore complementarity among views. Moreover, an effective optimization procedure based on the Alternating Direction Method of Multipliers scheme is utilized. Extensive experiments are carried out to evaluate the effectiveness of the proposed algorithm. The experimental results demonstrate that the proposed LRGO-MVDR algorithm outperforms related methods.

show abstract

Section: Discussionmentioning

confidence: 99%

Low-rank graph optimization for multi-view dimensionality reduction

et al. 2019

View full text Add to dashboard Cite

show abstract

“…where E denotes the sparse outliers and random noise and β 1 and β 2 are the trade-off parameter determining the importance of the corresponding term. Finally, the alternating direction method of multipliers (ADMM) [37] is adopted to solve the optimization problem (7).…”

Section: Introduction Of Spsdamentioning

confidence: 99%

Fault Diagnosis Method for Rolling Bearing Based on Sparse Principal Subspace Discriminant Analysis

Zhou

Zhu

2022

Shock and Vibration

View full text Add to dashboard Cite

Rolling bearings are omnipresent parts in industrial fields. To comprehensively reflect the status of rolling bearing and improve the classification accuracy, fusion information is widely used in various studies, which may result in high dimensionality, redundancy information of dataset, and time consumption. Thus, it is of crucial significance in extracting optimal features from high-dimensional and redundant feature space for classification. In this study, a fault diagnosis of rolling bearings model based on sparse principal subspace discriminant analysis is proposed. It extracts sparse discrimination information, meanwhile preserving the main energy of original dataset, and the sparse regularization term and sparse error term constrained by l2,1-norm are introduced to improve the performance of feature extraction and the robustness to noise and outliers. The multi-domain feature space involved a time domain, frequency domain, and time-frequency domain is first derived from the original vibration signals. Then, the intrinsic geometric features extracted by sparse principal subspace discriminant analysis are fed into a support vector machine classifier to recognize different operating conditions of bearings. The experimental results demonstrated that the feasibility and effectiveness of the proposed fault diagnosis model based on a sparse principal subspace discriminant analysis algorithm can achieve higher recognition accuracy than fisher discriminant analysis and its extensions, and it is relatively insensitive to the impact of noise and outliers owing to the sparse property.

show abstract

“…Their applicability to nonconvex problems has also been investigated, e.g., Diamond et al (2018). For nonconvex problems, while ADMM is not guaranteed to converge, in practice it can often find a reasonable objective value with small computational cost (Kanno and Kitayama 2018). It has been recently applied in structural optimization for problems with a few or hundreds of design variables.…”

Section: Introductionmentioning

confidence: 99%

“…It has been recently applied in structural optimization for problems with a few or hundreds of design variables. Kanno and Kitayama (2018) used ADMM as an effective heuristic for mixed-integer nonlinear structural optimization. Palanduz and Groenwold (2020) analyzed the applicability of a subset of ADMM-type algorithms for optimal structural design, in combination with a novel scaling method and quadratic approximations of the primal problem.…”

Section: Introductionmentioning

confidence: 99%

Alternating optimization of design and stress for stress-constrained topology optimization

Zhai

Chen

2021

Struct Multidisc Optim

View full text Add to dashboard Cite

Handling stress constraints is an important topic in topology optimization. In this paper, we introduce an interpretation of stresses as optimization variables, leading to an augmented Lagrangian formulation. This formulation takes two sets of optimization variables, i.e., an auxiliary stress variable per element, in addition to a density variable as in conventional density-based approaches. The auxiliary stress is related to the actual stress (i.e., computed by its definition) by an equality constraint. When the equality constraint is strictly satisfied, an upper bound imposed on the auxiliary stress design variable equivalently applies to the actual stress. The equality constraint is incorporated into the objective function as linear and quadratic terms using an augmented Lagrangian form. We further show that this formulation is separable regarding its two sets of variables. This gives rise to an efficient augmented Lagrangian solver known as the alternating direction method of multipliers (ADMM). In each iteration, the density variables, auxiliary stress variables, and Lagrange multipliers are alternatingly updated. The introduction of auxiliary stress variables enlarges the search space. We demonstrate the effectiveness and efficiency of the proposed formulation and solution strategy using simple truss examples and a dozen of continuum structure optimization settings.

show abstract

Alternating direction method of multipliers as a simple effective heuristic for mixed-integer nonlinear optimization

Cited by 15 publications

References 24 publications

Low-rank graph optimization for multi-view dimensionality reduction

Low-rank graph optimization for multi-view dimensionality reduction

Fault Diagnosis Method for Rolling Bearing Based on Sparse Principal Subspace Discriminant Analysis

Alternating optimization of design and stress for stress-constrained topology optimization

Contact Info

Product

Resources

About