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Sensitivity Analysis for Multiple Comparisons in Matched Observational Studies Through quadratically constrained Linear programming

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2016年第516期111卷 1820-1830页

作者： Fogarty, Colin B. Small, Dylan S. Univ Penn Wharton Sch Dept Stat Philadelphia PA 19104 USA MIT MIT Sloan Sch Management Cambridge MA 02142 USA MIT Ctr Operat Res Cambridge MA 02142 USA

A sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding. While sensitivity analyses in matched observational studies have been well addressed when there is a single outcome variable, accounting for multiple comparisons through the existing methods yields overly conservative results when there are multiple outcome variables of interest. This stems from the fact that unmeasured confounding cannot affect the probability of assignment to treatment differently depending on the outcome being analyzed. Existing methods allow this to occur by combining the results of individual sensitivity analyses to assess whether at least one hypothesis is significant, which in turn results in an overly pessimistic assessment of a study's sensitivity to unobserved biases. By solving a quadratically constrained linear program, we are able to perform a sensitivity analysis while enforcing that unmeasured confounding must have the same impact on the treatment assignment probabilities across outcomes for each individual in the study. We show that this allows for uniform improvements in the power of a sensitivity analysis not only for testing the overall null of no effect, but also for null hypotheses on specific outcome variables while strongly controlling the familywise error rate. We illustrate our method through an observational study on the effect of smoking on naphthalene exposure. Supplementary materials for this article are available online.

关键词： Causal inference Familywise error control Matching quadratically constrained programming Randomization inference Sensitivity analysis

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Optimization of Lens Adjustment in Semiconductor Lithography Equipment Using quadratically constrained and Second-Order Cone programming

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JOURNAL OF ADVANCED MECHANICAL DESIGN SYSTEMS AND MANUFACTURING 2010年第4期4卷 785-793页

作者： Shinano, Yuji Yoshihara, Toshiyuki Miyashiro, Ryuhei Fukagawa, Youzou Konrad Zuse Zentrum Informat Tech Berlin D-14195 Berlin Germany CANON INC Semicond Prod Equipment PLM Ctr 2 Utsunomiya Tochigi 3213292 Japan Tokyo Univ Agr & Technol Inst Engn Tokyo 1848588 Japan

The present paper considers optimization of lens adjustment in semiconductor lithography equipment. For improving productivity, the laser irradiation power of recent semiconductor lithography equipment has been boosted, which causes significant aberration due to heating during exposure. The aberration of the equipment must be measured or estimated in order to adjust the positions and orientations of the lenses. Since this adjustment is performed sequentially during exposure, the optimization problem to obtain optimal lens adjustment should be solved within a time as short as 100 ms. Although the problem of calculating the optimal lens adjustment can be naturally formulated as a convex minimization problem, in such a formulation the objective function is convex but includes several nondifferentiable points. Hence, optimization methods based on derivatives cannot be applied. Other approaches using derivative-free optimization or meta-heuristic methods cannot guarantee that the obtained solutions are truly optimal. Therefore, we formulate the optimization problem as quadratically constrained and second-order cone programming problems, which can be handled by solvers using an interior point method. Using the proposed formulations, computational experiments demonstrate that the optimal lens adjustment is obtained in a practical computational time, which is much less than 100 ms.

关键词： Semiconductor Lithography Aberration Optimum Design System Engineering Optical Instrument Precision Instrument Second Order Cone programming quadratically constrained programming Engineering Optimization

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A Heuristic algorithm to solve the unit commitment problem for real-life large-scale power systems

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2013年第1期49卷 287-295页

作者： Alvarez Lopez, Juan Ceciliano-Meza, Jose L. Guillen, Isaias Nieva Gomez, Rolando Elect Res Inst Network Anal Dept Cuernavaca 62490 Morelos Mexico Elect Res Inst Elect Syst Div Cuernavaca 62490 Morelos Mexico

One of the main needs that power system operators around the world have is to solve complex Unit Commitment models for large-scale power systems in an acceptable computation time. This Paper presents an alternative Heuristic algorithm that successfully addresses this need. The Heuristic algorithm makes use of various optimization techniques such as Mixed Integer Linear programming (MILP), Quadratic programming (QP), quadratically constrained programming (QCP), and Dynamic programming (DP). CPLEX 12.2 is used as the main optimization engine for MILP, QP, and QCP. DP is an in-house algorithm used to obtain the commitment of Combined Cycle Plants (CCPs) when represented with the component-based model. This Heuristic algorithm combines the global optimality capabilities of MI (L) P formulations with the highly detailed models available for CCPs using LR-DP formulations. The Heuristic algorithm introduced in this Paper is capable of solving up to 1-week scenarios with a 1-hour time window for the complex Mexican Power System. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： CPLEX Dynamic programming Mixed integer linear programming quadratically constrained programming Quadratic programming Unit commitment

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Optimizing Instantaneous and Ramping Reserves With Different Response Speeds for Contingencies-Part II: Implications

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IEEE TRANSACTIONS ON POWER SYSTEMS 2020年第5期35卷 3961-3969页

作者： Schipper, Josh Wood, Alan Edwards, Conrad Univ Canterbury Dept Elect & Comp Engn Christchurch 8041 New Zealand Univ Canterbury Elect Power Engn Ctr Christchurch 8041 New Zealand Transpower Wellington 6011 New Zealand

Part I presents a formulation to optimize reserves for contingent events while explicitly including their response times. Part II highlights the implications of using this formulation in a reserves market. There are four aspects of the formulation that are of interest: (1) the performance of the solver, (2) the importance of inertia and contingency size. These implications are highlighted through two examples. (3) The proposed formulation is compared against a reserve optimization which does not distinguish between different response speeds, but adjusts the reserve requirement to satisfy the same frequency limits. Differentiating between response speeds within the optimization can provide a 23% reduction in total reserve requirement on average, which improves to a reduction of 52% in low inertia conditions. (4) A marginal pricing methodology is developed which prices reserve in a market context, and gives a unique price to each reserve provider depending on response speed. This gives incentive for reserve providers to improve response speed.

关键词： Time-frequency analysis Optimization Power systems Transient analysis Pricing Time factors Reserve markets primary frequency control reserve contingency reserve quadratically constrained programming convex optimization

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Multi-way clustering and biclustering by the Ratio cut and Normalized cut in graphs

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2012年第2期23卷 224-251页

作者： Fan, Neng Pardalos, Panos M. Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA

In this paper, we consider the multi-way clustering problem based on graph partitioning models by the Ratio cut and Normalized cut. We formulate the problem using new quadratic models. Spectral relaxations, new semidefinite programming relaxations and linearization techniques are used to solve these problems. It has been shown that our proposed methods can obtain improved solutions. We also adapt our proposed techniques to the bipartite graph partitioning problem for biclustering.

关键词： Ratio cut Normalized cut Clustering Biclustering Graph partitioning Spectral relaxation Semidefinite programming quadratically constrained programming

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Inverse Reinforcement Learning in Partially Observable Environments

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JOURNAL OF MACHINE LEARNING RESEARCH 2011年第3期12卷 691-730页

作者： Choi, Jaedeug Kim, Kee-Eung Korea Adv Inst Sci & Technol Dept Comp Sci Taejon 305701 South Korea

Inverse reinforcement learning (IRL) is the problem of recovering the underlying reward function from the behavior of an expert. Most of the existing IRL algorithms assume that the environment is modeled as a Markov decision process (MDP), although it is desirable to handle partially observable settings in order to handle more realistic scenarios. In this paper, we present IRL algorithms for partially observable environments that can be modeled as a partially observable Markov decision process (POMDP). We deal with two cases according to the representation of the given expert's behavior, namely the case in which the expert's policy is explicitly given, and the case in which the expert's trajectories are available instead. The IRL in POMDPs poses a greater challenge than in MDPs since it is not only ill-posed due to the nature of IRL, but also computationally intractable due to the hardness in solving POMDPs. To overcome these obstacles, we present algorithms that exploit some of the classical results from the POMDP literature. Experimental results on several benchmark POMDP domains show that our work is useful for partially observable settings.

关键词： inverse reinforcement learning partially observable Markov decision process inverse optimization linear programming quadratically constrained programming

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Clustering categories in support vector machines

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2017年第PartA期66卷 28-37页

作者： Carrizosa, Emilio Nogales-Gomez, Amaya Morales, Dolores Romero Univ Seville Fac Matemat Dept Estadist & Invest Operat Seville Spain Huawei France R&D Math & Algorithm Sci Lab Paris France Copenhagen Business Sch Dept Econ Copenhagen Denmark

The support vector machine (SVM) is a state-of-the-art method in supervised classification. In this paper the Cluster Support Vector Machine (CLSVM) methodology is proposed with the aim to increase the sparsity of the SVM classifier in the presence of categorical features, leading to a gain in interpretability. The CLSVM methodology clusters categories and builds the SVM classifier in the clustered feature space. Four strategies for building the CLSVM classifier are presented based on solving: the SVM formulation in the original feature space, a quadratically constrained quadratic programming formulation, and a mixed integer quadratic programming formulation as well as its continuous relaxation. The computational study illustrates the performance of the CLSVM classifier using two clusters. In the tested datasets our methodology achieves comparable accuracy to that of the SVM in the original feature space, with a dramatic increase in sparsity. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Support vector machine Categorical features Classifier sparsity Clustering quadratically constrained programming 0-1 programming

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AC OPF for Smart Distribution Networks: An Efficient and Robust Quadratic Approach

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IEEE TRANSACTIONS ON SMART GRID 2018年第5期9卷 4613-4623页

作者： Franco, John F. Ochoa, Luis F. Romero, Ruben Univ Estadual Paulista UNESP BR-19274000 Rosana Brazil Univ Melbourne Dept Elect & Elect Engn Parkville Vic 3010 Australia Univ Manchester Sch Elect & Elect Engn Manchester M13 9PL Lancs England Univ Estadual Paulista UNESP Fac Engn Ilha Solteira BR-15385000 Ilha Solteira Brazil

Smart grid schemes in which multiple network elements and participants are managed for the benefit of the distribution network (e.g., energy loss reduction, restoration, etc.) require sophisticated algorithms to control them in the most suitable manner while catering for network constraints. Such a complex decision making process can be solved by tailoring the ac optimal power flow (OPF) problem to the corresponding smart grid scheme. Non-linear programming ac OPF formulations, however, can suffer from scalability and robustness issues which in turn might limit their adoption. Here, a novel quadratic programming formulation is proposed and compared against the non-linear, quadratically constrained, and linearized approaches. Two cases are carried out to assess their performance: 1) management of distributed generation units to maximize renewable energy harvesting (continuous control variables) and 2) control of capacitors to minimize energy losses (discrete control variables). The results demonstrate that the proposed quadratic approach significantly outperforms the more conventional formulations in both computational efficiency and robustness. This makes it a suitable alternative to be at the heart of the decision making of complex, real-time schemes to be adopted by future smart distribution networks.

关键词： Distribution networks non-linear programming optimal power flow quadratically constrained programming quadratic programming smart grids

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Optimal design of Hermitian transform and vectors of both mask and window coefficients for denoising applications with both unknown noise characteristics and distortions

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SIGNAL PROCESSING 2014年 98卷 1-22页

作者： Ling, Bingo Wing-Kuen Ho, Charlotte Yuk-Fan Subramaniam, Suba R. Georgakis, Apostolos Cao, Jiangzhong Dai, Qingyun Guangdong Univ Technol Fac Informat Engn Guangzhou 510006 Guangdong Peoples R China Hong Kong Polytech Univ Dept Elect & Informat Engn Hong Kong Hong Kong Peoples R China Kings Coll London Div Engn Dept Elect Engn London WC2R 2LS England

This paper proposes an optimal design of a Hermitian transform and vectors of both mask and window coefficients for denoising signals with both unknown noise characteristics and distortions. The signals are represented in the vector form. Then, they are transformed to a new domain via multiplying these vectors to a Hermitian matrix. A vector of mask coefficients is point by point multiplied to the transformed vectors. The processed vectors are transformed back to the time domain. A vector of window coefficients is point by point multiplied to the processed vectors. An optimal design of the Hermitian matrix and the vectors of both mask and window coefficients is formulated as a quadratically constrained programming problem subject to a Hermitian constraint. By initializing the window coefficients, the Hermitian matrix and the vector of mask coefficients are derived via an orthogonal Procrustes approach. Based on the obtained Hermitian matrix and the vector of mask coefficients, the vector of window coefficients is derived. By iterating these two procedures, the final Hermitian matrix and the vectors of both mask and window coefficients are obtained. The convergence of the algorithm is guaranteed. The proposed method is applied to denoise both clinical electrocardiograms and electromyograms as well as speech signals with both unknown noise characteristics and distortions. Experimental results show that the proposed method outperforms existing denoising methods. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Hermitian transform Mask operation Windowing quadratically constrained programming Quadratic complex valued matrix equality constraint Orthogonal Procrustes

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Modeling zonal exchanges and nodal system representation in multi-zonal spot electricity markets

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ELECTRIC POWER SYSTEMS RESEARCH 2021年 196卷 107172-107172页

作者： Vlachos, Andreas G. Biskas, Pandelis N. Aristotle Univ Thessaloniki Sch Elect & Comp Engn Thessaloniki Greece

A novel model for the solution of the flow-based market coupling problem in multi-zonal spot electricity markets with zonal exchanges is presented in this paper. The problem considers a hybrid network configuration, i.e. a zonal market layer with zonal portfolio offers / bids submitted by the participants and zonal market clearing prices, and a nodal physical layer with nodal representation of the transmission system flows and relevant constraints. The model provides the optimal supply / demand cleared quantities and zonal exchanges, endogenously bounded by grid physical constraints, e.g. branch physical limits. The model retains the intuitiveness of the zonal exchanges, namely exchanges are cleared only from low-price zones to high-price zones. The model exhibits a dynamic/optimal allocation of zonal to nodal volumes. This market setup is fully compliant with the current market design in Europe, where portfolio participation in spot market with zonal prices, intuitive exchanges and with nodal flow-based constraints is the preferred scheme of the European Commission based on Regulation 2015/1222. The model is compared in terms of overall social welfare, pricing and cleared exchanges with the currently applied approach in Europe plus a "tuning" model for the simulation of redispatching to avoid congestion in physical branches.

关键词： Flow-based Intuitive exchanges quadratically constrained programming Complementarity conditions Nodal system representation Zonal exchanges Zonal clearing prices

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