Parameter identification of quasibrittle materials as a mathematical program with equilibrium constraints

2001 ◽  
Vol 190 (43-44) ◽  
pp. 5819-5836 ◽  
Author(s):  
F Tin-Loi ◽  
N.S Que
Keyword(s):  
Parameter Identification ◽  
Mathematical Program ◽  
Equilibrium Constraints ◽  
Quasibrittle Materials

Capturing Electricity Market Dynamics in the Optimal Trading of Strategic Agents using Neural Network Constrained Optimization

2021 ◽  
Author(s):  
Mihály Dolányi ◽  
Kenneth Bruninx ◽  
Jean-François Toubeau ◽  
Erik Delarue
Keyword(s):  
Neural Network ◽  
Electricity Markets ◽  
Electricity Market ◽  
Mathematical Program ◽  
Market Dynamics ◽  
Equilibrium Constraints ◽  
Market Outcomes ◽  
Optimal Trading ◽  
Optimal Bidding ◽  
Upper Level

In competitive electricity markets the optimal trading problem of an electricity market agent is commonly formulated as a bi-level program, and solved as mathematical program with equilibrium constraints (MPEC). In this paper, an alternative paradigm, labeled as mathematical program with neural network constraint (MPNNC), is developed to incorporate complex market dynamics in the optimal bidding strategy. This method uses input-convex neural networks (ICNNs) to represent the mapping between the upper-level (agent) decisions and the lower-level (market) outcomes, i.e., to replace the lower-level problem by a neural network. In a comparative analysis, the optimal bidding problem of a load agent is formulated via the proposed MPNNC and via the classical bi-level programming method, and compared against each other.

scholarly journals Global and Local Tensor Sparse Approximation Models for Hyperspectral Image Destriping

2020 ◽  
Vol 12 (4) ◽  
pp. 704 ◽  
Author(s):  
Xiangyang Kong ◽  
Yongqiang Zhao ◽  
Jize Xue ◽  
Jonathan Cheung-Wai Chan ◽  
Seong G. Kong
Keyword(s):  
Convex Function ◽  
Hyperspectral Image ◽  
Mathematical Program ◽  
Sparse Approximation ◽  
Hyperspectral Images ◽  
Equilibrium Constraints ◽  
Spectral Distortion ◽  
Spectral Correlation ◽  
Evaluation Measures ◽  
Global And Local

This paper presents a global and local tensor sparse approximation (GLTSA) model for removing the stripes in hyperspectral images (HSIs). HSIs can easily be degraded by unwanted stripes. Two intrinsic characteristics of the stripes are (1) global sparse distribution and (2) local smoothness along the stripe direction. Stripe-free hyperspectral images are smooth in spatial domain, with strong spectral correlation. Existing destriping approaches often do not fully investigate such intrinsic characteristics of the stripes in spatial and spectral domains simultaneously. Those methods may generate new artifacts in extreme areas, causing spectral distortion. The proposed GLTSA model applies two ℓ 0 -norm regularizers to the stripe components and along-stripe gradient to improve the destriping performance. Two ℓ 1 -norm regularizers are applied to the gradients of clean image in spatial and spectral domains. The double non-convex functions in GLTSA are converted to single non-convex function by mathematical program with equilibrium constraints (MPEC). Experiment results demonstrate that GLTSA is effective and outperforms existing competitive matrix-based and tensor-based destriping methods in visual, as well as quantitative, evaluation measures.

scholarly journals A Proximal Algorithm with Convergence Guarantee for a Nonconvex Minimization Problem Based on Reproducing Kernel Hilbert Space

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2393
Author(s):  
Hong-Xia Dou ◽  
Liang-Jian Deng
Keyword(s):  
Hilbert Space ◽  
Minimization Problem ◽  
Reproducing Kernel ◽  
Mathematical Program ◽  
Reproducing Kernel Hilbert Space ◽  
Reproducing Kernels ◽  
Equilibrium Constraints ◽  
Nonconvex Minimization ◽  
Ill Posed ◽  
The Given

The underlying function in reproducing kernel Hilbert space (RKHS) may be degraded by outliers or deviations, resulting in a symmetry ill-posed problem. This paper proposes a nonconvex minimization model with ℓ0-quasi norm based on RKHS to depict this degraded problem. The underlying function in RKHS can be represented by the linear combination of reproducing kernels and their coefficients. Thus, we turn to estimate the related coefficients in the nonconvex minimization problem. An efficient algorithm is designed to solve the given nonconvex problem by the mathematical program with equilibrium constraints (MPEC) and proximal-based strategy. We theoretically prove that the sequences generated by the designed algorithm converge to the nonconvex problem’s local optimal solutions. Numerical experiment also demonstrates the effectiveness of the proposed method.

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