We consider a robust phase retrieval problem that aims to recover a signal from its absolute measurements corrupted with sparse noise. The least absolute deviation (LAD) provides a robust estimation against outliers. ...
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ISBN:
(纸本)9798350344868;9798350344851
We consider a robust phase retrieval problem that aims to recover a signal from its absolute measurements corrupted with sparse noise. The least absolute deviation (LAD) provides a robust estimation against outliers. However, the corresponding optimization problem is nonconvex. We propose an "unregularized" iterative convexification approach to LAD through a sequence of linear programs (SLP). We provide a non-asymptotic convergence analysis under the standard Gaussian assumption of the measurement vectors. The SLP algorithm, when suitably initialized, linearly converges to the ground truth at optimal sample complexity up to a numerical constant. Furthermore, SLP empirically outperforms existing methods that provide a comparable performance guarantee.
We show that given a feasible primal-dual pair of linear programs in canonical form, there exists a sequence of pivots, whose length is bounded by the minimum dimension of the constraint matrix, leading from the origi...
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We show that given a feasible primal-dual pair of linear programs in canonical form, there exists a sequence of pivots, whose length is bounded by the minimum dimension of the constraint matrix, leading from the origin to the optimum. The sequence of pivots give a sequence of square and nonsingular submatrices of the constraint matrix. Solving two linear equations involving such a submatrix give primal-dual optimal solutions to the corresponding linear program in canonical form. (C) 2020 The Authors. Published by Elsevier B.V.
We introduce the SqueezeFit linear program as a fast and robust dimensionality reductionmethod. This program is inspired by both the SqueezeFit semi-definite program [10] andscGeneFit [3], which is a linear program ve...
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We introduce the SqueezeFit linear program as a fast and robust dimensionality reductionmethod. This program is inspired by both the SqueezeFit semi-definite program [10] andscGeneFit [3], which is a linear program version of SqueezeFit that has been used to classifysingle cell RNA-sequence data with a given structured partition. The original SqueezeFitsemi-definite program has a strong theoretical background but it exhibits slow runtimes withlarge data sets. In contrast, scGeneFit performs efficiently and robustly with scRNA-seqdata given either flat or hierarchical label partitions, but it does not have much theoreticaljustification for its performance. The SqueezeFit linear program fills this computational andtheoretical gap. After providing new theoretical guarantees, we illustrate the performanceof the SqueezeFit linear program on real-world gene expression data.
A modular multilevel converter contains many capacitor full-bridge converter cells. An increased capacitance in the converter means a large overall converter size and increased converter cost. Previous research has in...
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ISBN:
(纸本)9781728126586
A modular multilevel converter contains many capacitor full-bridge converter cells. An increased capacitance in the converter means a large overall converter size and increased converter cost. Previous research has investigated methods to reduce converter cell capacitance. One paper presents an iterative linear program to reduce the capacitance while limiting the average currents. The work presented in this paper modifies the linear program to further reduce average currents for similar reduction in capacitance. Furthermore, the results presented here show root-mean-square currents will also be reduced.
A modular multilevel converter contains many capacitor full-bridge converter cells. An increased capacitance in the converter means a large overall converter size and increased converter cost. Previous research has in...
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ISBN:
(数字)9781728126586
ISBN:
(纸本)9781728126593
A modular multilevel converter contains many capacitor full-bridge converter cells. An increased capacitance in the converter means a large overall converter size and increased converter cost. Previous research has investigated methods to reduce converter cell capacitance. One paper presents an iterative linear program to reduce the capacitance while limiting the average currents. The work presented in this paper modifies the linear program to further reduce average currents for similar reduction in capacitance. Furthermore, the results presented here show root-mean-square currents will also be reduced.
The pattern of water use operation is important to ensure the continuity of water supply system of a reservoir. This pattern, which is usually called power rule curve in a hydropower system, should be optimally obtain...
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The pattern of water use operation is important to ensure the continuity of water supply system of a reservoir. This pattern, which is usually called power rule curve in a hydropower system, should be optimally obtained, so that the yielded electrical power also becomes optimal while the continuity of reservoir storage can also be tenable. In this study, in order to satisfy the main objective of Riam Jerawi Reservoir, where the energy of 6 MW should be provided every month, a linear optimization model is applied for three objective functions such as maximizing total energy, maximizing minimum energy and minimizing energy shortage. In addition, a simulation model is also presented for comparison purpose particularly to emphasize some disadvantages of using this model. The results show that the optimum energy can be achieved by applying this optimization model where the continuity of reservoir volume is also satisfied. Meanwhile, the simulation model produces the rule curve, which cannot satisfy the continuity criterion. This optimization model is expected to be applied for other similar cases and give the optimum power rule curve for the related stakeholders.
In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and o...
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In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions depend on the answer sets of conjunctive queries. We contribute an efficient algorithm for solving programs in a fragment of LP(CQ). The natural approach constructs a linear program having as many variables as there are elements in the answer set of the queries. Our approach constructs a linear program having the same optimal value but fewer variables. This is done by exploiting the structure of the conjunctive queries using generalized hypertree decompositions of small width to factorize elements of the answer set together. We illustrate the various applications of LP(CQ) programs on three examples: optimizing deliveries of resources, minimizing noise for differential privacy, and computing the s -measure of patterns in graphs as needed for data mining.
This paper presents the properties of the minimum mean cycle-canceling algorithm for solving linear programming models. Originally designed for solving network flow problems for which it runs in strongly polynomial ti...
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This paper presents the properties of the minimum mean cycle-canceling algorithm for solving linear programming models. Originally designed for solving network flow problems for which it runs in strongly polynomial time, most of its properties are preserved. This is at the price of adapting the fundamental decomposition theorem of a network flow solution together with various definitions: that of a cycle and the way to calculate its cost, the residual problem, and the improvement factor at the end of a phase. We also use the primal and dual necessary and sufficient optimality conditions stated on the residual problem for establishing the pricing step giving its name to the algorithm. It turns out that the successive solutions need not be basic, there are no degenerate pivots, and the improving directions are potentially interior in addition to those on edges. For solving an m x n linear program, it requires a pseudo-polynomial number O (n A) of so-called phases, where A depends on the number of rows and the coefficient matrix. (c) 2021 Elsevier B.V. All rights reserved.
This article shows how to solve linear programs of the form min(Ax=b,x) (>= 0) c(inverted perpendicular)x with n variables in time O*((n(omega) + n(2.5-alpha/2) + n(2+1/6)) log(n/delta)), where omega is the exponen...
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This article shows how to solve linear programs of the form min(Ax=b,x) (>= 0) c(inverted perpendicular)x with n variables in time O*((n(omega) + n(2.5-alpha/2) + n(2+1/6)) log(n/delta)), where omega is the exponent of matrix multiplication, alpha is the dual exponent of matrix multiplication, and delta is the relative accuracy. For the current value of omega similar to 2.37 and alpha similar to 0.31, our algorithm takes O* (n(omega)log(n/delta)) time. When omega = 2, our algorithm takes O* (n(2+1/6) log(n/delta)) time. Our algorithm utilizes several new concepts that we believe may be of independent interest: We define a stochastic central path method. We show how to maintain a projection matrix root WA(inverted perpendicular) (AWA(inverted perpendicular))(-1)A root W in sub-quadratic time under l(2) multiplicative changes in the diagonal matrix W.
Influence maximization is an important research topic in social networks that has different applications such as analyzing spread of rumors, interest, adoption of innovations, and feed ranking. The goal is to select a...
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Influence maximization is an important research topic in social networks that has different applications such as analyzing spread of rumors, interest, adoption of innovations, and feed ranking. The goal is to select a limited size subset of vertices (called a seed-set) in a Social Graph, so that upon their activation, a maximum number of vertices of the graph become activated, due to the influence of the vertices on each other. The linear threshold model is one of two classic stochastic propagation models that describe the spread of influence in a network. We present a new approach called MLPR (matrix multiplication, linear programming, randomized rounding) with linear programming used as its core in order to solve the influence maximization problem in the linear threshold model. Experiments on four real data sets have shown the efficiency of the MLPR method in solving the influence maximization problem in the linear threshold model. The spread of the output seed-sets is as large as when the state-of-the-art algorithms are used;however, unlike most of the existing algorithms, the runtime of our method is independent of the seed size and does not increase with it.
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