Lipschitz Optimization

2000 ◽  
pp. 237-265
Author(s):  
Reiner Horst ◽  
Panos M. Pardalos ◽  
Nguyen V. Thoai
Keyword(s):  
Lipschitz Optimization

Convergence of ℓ2/3 Regularization for Sparse Signal Recovery

2015 ◽  
Vol 32 (04) ◽  
pp. 1550023 ◽  
Author(s):  
Lu Liu ◽  
Di-Rong Chen
Keyword(s):  
Fixed Point ◽  
Large Scale ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Lipschitz Optimization ◽  
Iterative Thresholding ◽  
Point Representation ◽  
Iterative Thresholding Algorithm ◽  
Thresholding Algorithm

In this paper, we consider the problem of finding the sparsest solution to underdetermined linear systems. Unlike the literatures which use the ℓ1 regularization to approximate the original problem, we consider the ℓ2/3 regularization which leads to a better approximation but a nonconvex, nonsmooth, and non-Lipschitz optimization problem. Through developing a fixed point representation theory associated with the two thirds thresholding operator for ℓ2/3 regularization solutions, we propose a fixed point iterative thresholding algorithm based on two thirds norm for solving the k-sparsity problems. Relying on the restricted isometry property, we provide subsequentional convergence guarantee for this fixed point iterative thresholding algorithm on recovering a sparse signal. By discussing the preferred regularization parameters and studying the phase diagram, we get an adequate and efficient algorithm for the high-dimensional sparse signal recovery. Finally, comparing with the existing algorithms, such as the standard ℓ1 minimization, the iterative reweighted ℓ2 minimization, the iterative reweighted ℓ1 minimization, and iterative Half thresholding algorithm, we display the results of the experiment which indicate that the two thirds norm fixed point iterative thresholding algorithm applied to sparse signal recovery and large scale imageries from noisy measurements can be accepted as an effective solver for ℓ2/3 regularization.

scholarly journals Inventory Model with Partial Backordering When Backordered Customers Delay Purchase after Stockout-Restoration

2016 ◽  
Vol 2016 ◽  
pp. 1-16
Author(s):  
Ren-Qian Zhang ◽  
Yan-Liang Wu ◽  
Wei-Guo Fang ◽  
Wen-Hui Zhou
Keyword(s):  
Layer Structure ◽  
Inventory Model ◽  
Inventory Cost ◽  
Cost Component ◽  
Lipschitz Optimization ◽  
Partial Backordering ◽  
Demand Rate ◽  
Holding Cost ◽  
Total Inventory ◽  
Inventory Holding

Many inventory models with partial backordering assume that the backordered demand must be filled instantly after stockout restoration. In practice, however, the backordered customers may successively revisit the store because of the purchase delay behavior, producing a limited backorder demand rate and resulting in an extra inventory holding cost. Hence, in this paper we formulate the inventory model with partial backordering considering the purchase delay of the backordered customers and assuming that the backorder demand rate is proportional to the remaining backordered demand. Particularly, we model the problem by introducing a new inventory cost component of holding the backordered items, which has not been considered in the existing models. We propose an algorithm with a two-layer structure based on Lipschitz Optimization (LO) to minimize the total inventory cost. Numerical experiments show that the proposed algorithm outperforms two benchmarks in both optimality and efficiency. We also observe that the earlier the backordered customer revisits the store, the smaller the inventory cost and the fill rate are, but the longer the order cycle is. In addition, if the backordered customers revisit the store without too much delay, the basic EOQ with partial backordering approximates our model very well.

scholarly journals Optimality of Radio Power Control Via Fast-Lipschitz Optimization

2016 ◽  
Vol 64 (6) ◽  
pp. 2589-2601 ◽  
Author(s):  
Carlo Fischione ◽  
Martin Jakobsson
Keyword(s):  
Power Control ◽  
Lipschitz Optimization ◽  
Radio Power

scholarly journals Comparison of Feature Selection Techniques for Power Amplifier Behavioral Modeling and Digital Predistortion Linearization

Sensors ◽  
2021 ◽  
Vol 21 (17) ◽  
pp. 5772
Author(s):  
Abdoul Barry ◽  
Wantao Li ◽  
Juan A. Becerra ◽  
Pere L. Gilabert
Keyword(s):  
Power Amplifier ◽  
Power Efficiency ◽  
Volterra Series ◽  
Matching Pursuit ◽  
Order Reduction ◽  
Orthogonal Matching Pursuit ◽  
Hill Climbing ◽  
Digital Predistortion ◽  
Lipschitz Optimization ◽  
Reduction Techniques

The power amplifier (PA) is the most critical subsystem in terms of linearity and power efficiency. Digital predistortion (DPD) is commonly used to mitigate nonlinearities while the PA operates at levels close to saturation, where the device presents its highest power efficiency. Since the DPD is generally based on Volterra series models, its number of coefficients is high, producing ill-conditioned and over-fitted estimations. Recently, a plethora of techniques have been independently proposed for reducing their dimensionality. This paper is devoted to presenting a fair benchmark of the most relevant order reduction techniques present in the literature categorized by the following: (i) greedy pursuits, including Orthogonal Matching Pursuit (OMP), Doubly Orthogonal Matching Pursuit (DOMP), Subspace Pursuit (SP) and Random Forest (RF); (ii) regularization techniques, including ridge regression and least absolute shrinkage and selection operator (LASSO); (iii) heuristic local search methods, including hill climbing (HC) and dynamic model sizing (DMS); and (iv) global probabilistic optimization algorithms, including simulated annealing (SA), genetic algorithms (GA) and adaptive Lipschitz optimization (adaLIPO). The comparison is carried out with modeling and linearization performance and in terms of runtime. The results show that greedy pursuits, particularly the DOMP, provide the best trade-off between execution time and linearization robustness against dimensionality reduction.

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