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A New Mathematical Approach in Environmental and Life Sciences: Gene-Environment Networks and Their Dynamics

ENVIRONMENTAL MODELING & ASSESSMENT 2009年第2期14卷 267-288页

作者： Weber, G. -W. Alparslan-Gok, S. Z. Soyler, B. Middle E Tech Univ Inst Appl Math TR-06531 Ankara Turkey Suleyman Demirel Univ Fac Arts & Sci Dept Math TR-32260 Isparta Turkey Middle E Tech Univ Dept Food Engn TR-06531 Ankara Turkey

An important research area in life sciences is devoted to modeling, prediction, and dynamics of gene-expression patterns. As clearly understood in these days, this enterprise cannot become satisfactory without acknowledging the role of the environment. To a representation of past, present, and most likely future states, we also encounter measurement errors and uncertainties. This paper surveys and improves recent advances in understanding the foundations and interdisciplinary implications of the newly introduced gene-environment networks, and it integrates the important theme of carbon dioxide emission reduction into the networks and dynamics. We also introduce some operational and managerial issues of practical working and decision making, expressed in terms of sliding windows, quadrants (modules) of parametric effects, and navigating (controlling) between such effects and directing them. Given data from DNA microarray experiments and environmental records, we extract nonlinear ordinary differential equations that contain parameters that have to be determined. For this, we employ modern (Chebychevian) approximation and (generalized semi-infinite) optimization. After this is provided, time- discretized dynamical systems are studied. A combinatorial algorithm with polyhedra sequences allows to detect the region of parametric stability. Finally, we analyze the topological landscape of gene-environment networks with its structural (in)stability. By embedding as a module and investigating CO2 emission control and figuring out game theoretical aspects, we conclude. This pioneering work is theoretically elaborated, practically devoted to health care, medicine, education, living conditions, and environmental protection, and it invites the readers to future research.

关键词： Environment Computational biology Errors Uncertainty Modeling Dynamics Intervals Matrices Stability Approximation GSIP Games Topology conic programming

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Evaluating port efficiency dynamics: A risk-based approach

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2022年 166卷 333-347页

作者： Sun, Qinghe Chen, Li Meng, Qiang Hong Kong Polytech Univ Dept Logist & Maritime Studies Kowloon Hong Kong Peoples R China Natl Univ Singapore Inst Operat Res & Analyt Singapore 117602 Singapore Natl Univ Singapore Dept Civil & Environm Engn Singapore 117576 Singapore

This study proposes a new methodology to quantify the efficiency dynamics of a port over time. While efficiency evaluation has gained full attention in port management, researchers conduct-ing related studies are challenged by temporal variations observed in the collected data. Existing approaches have almost exclusively relied on multivariate normal distributional assumptions of the input and output data, but empirical evidence from real data shows that the port operations data demonstrate long-tail distributions and violate the distributional assumptions. In addition, many existing models are intractable (non-convex) or lack interpretability. Motivated by these challenges, we develop an optimization-based approach for efficiency measurement under uncertainty that is compatible with the conventional non-parametric method. In particular, inspired by the coherent risk measure, we create a risk-based index to measure the efficiency of any operating unit by comparing its observations against a benchmark that is guaranteed to be production possible under a certain risk level. To facilitate the computation of the index, we develop a risk-based port efficiency evaluation (RPE) model, which can be reformulated as an exponential cone program (ECP) and solved efficiently by off-the-shelf solvers. We test our model for a multipurpose port on a real dataset of 3,394 observations showing the proposed approach's merits. We find that the port productivity peaks on Tuesday and Saturday and troughs on Friday. We also provide evidence for the Chinese New Year effect from a port management perspective and draw managerial insights from the study.

关键词： Port efficiency Stochastic efficiency Risk measure conic programming

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FAST METHODS FOR COMPUTING THE p-RADIUS OF MATRICES

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2011年第3期33卷 1246-1266页

作者： Jungers, Raphael M. Protasov, Vladimir Y. MIT Informat & Decis Syst Lab Cambridge MA 02139 USA Moscow MV Lomonosov State Univ Dept Mech & Math Moscow 119992 Russia

The p-radius characterizes the average rate of growth of norms of matrices in a multiplicative semigroup. This quantity has found several applications in recent years. We raise the question of its computability. We prove that the complexity of its approximation increases exponentially with p. We then describe a series of approximations that converge to the p-radius with a priori computable accuracy. For nonnegative matrices, this gives efficient approximation schemes for the p-radius computation.

关键词： joint spectral radius p-radius approximation algorithm conic programming smoothness in L-p spaces

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SELF-CONCORDANCE AND DECOMPOSITION-BASED INTERIOR POINT METHODS FOR THE TWO-STAGE STOCHASTIC CONVEX OPTIMIZATION PROBLEM

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SIAM JOURNAL ON OPTIMIZATION 2011年第4期21卷 1667-1687页

作者： Chen, Michael Mehrotra, Sanjay York Univ Dept Math & Stat Toronto ON M3J 1P3 Canada York Univ Dept Math & Stat Toronto ON M3J 1P3 Canada Northwestern Univ Dept IE MS Evanston IL 60208 USA

We study the two-stage stochastic convex optimization problem whose first-and second-stage feasible regions admit a self-concordant barrier. We show that the barrier recourse functions and the composite barrier functions for this problem form self-concordant families. These results are used to develop prototype primal interior point decomposition algorithms that are more suitable for a heterogeneous distributed computing environment. We show that the worst case iteration complexity of the proposed algorithms is the same as that for the short-and long-step primal interior algorithms applied to the extensive formulation of this problem. The generality of our results allows the possibility of using barriers other than the standard log-barrier in an algorithmic framework.

关键词： stochastic programming convex programming conic programming Benders' decomposition interior point methods

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A computational homogenization for yield design of asymmetric microstructures using adaptive bES-FEM

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COMPUTERS & STRUCTURES 2024年 294卷

作者： Ho, Phuc L. H. Lee, Changkye Le, Canh, V Nguyen, Phuong H. Yee, Jurng-Jae Dong A Univ Univ Core Res Ctr Disaster Free & Safe Ocean City Busan 49315 South Korea Int Univ Sch Civil Engn & Management Ho Chi Minh City Vietnam Vietnam Natl Univ Ho Chi Minh City Vietnam

This study presents a robust numerical method for the computational homogenization analysis of microstructures at limit state. The periodic boundary conditions for asymmetric meshes are effectively handled using piecewise cubic Hermite interpolation. The accuracy of the numerical results is greatly enhanced through the utilization of the edge -based smoothed finite element method (ES-FEM) enriched with a cubic bubble function. The bubbleenhanced ES-FEM (bES-FEM) is also able to avoid volumetric locking induced by the incompressibility constraints in plane strain limit analysis. The optimization problem is formulated as conic programming and is rapidly solved using primal -dual interior point -based software packages. Adaptive mesh refinement offers substantial benefits in reducing computational costs and predicting the failure mechanism of microscopic heterogeneous materials. The interaction surface of the effective macroscopic strengths can also be rapidly and directly obtained. Investigation of various representative volume elements (RVE) with arbitrary mesh designs demonstrates the computational efficacy of the proposed method.

关键词： Limit analysis Homogenization analysis conic programming bES-FEM Adaptive refinement

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A STRONG DUAL FOR conic MIXED-INTEGER PROGRAMS

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SIAM JOURNAL ON OPTIMIZATION 2012年第3期22卷 1136-1150页

作者： Moran R, Diego A. Dey, Santanu S. Vielma, Juan Pablo Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA Univ Pittsburgh Dept Ind Engn Pittsburgh PA 15260 USA

Mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension of the duality theory for mixed-integer linear programming (see [M. Guzelsoy and T. K. Ralphs, Int. J. Oper. Res. (Taichung), 4 (2007), pp. 118-137], [G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization, Wiley-Interscience, New York, 1988]) to the case of mixed-integer conic programming. In particular, we construct a subadditive dual for mixed-integer conic programming problems. Under a simple condition on the primal problem, we show that strong duality holds.

关键词： mixed-integer nonlinear programming conic programming duality cutting planes

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Optimal location-allocation of storage devices and renewable-based DG in distribution systems

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ELECTRIC POWER SYSTEMS RESEARCH 2019年第Jul.期172卷 11-21页

作者： Home-Ortiz, Juan M. Pourakbari-Kasmaei, Mahdi Lehtonen, Matti Sanches Mantovani, Jose Roberto Sao Paulo State Univ UNESP Dept Elect Engn Ilha Solteira SP Brazil Aalto Univ Dept Elect Engn & Automat Maarintie 8 Espoo 02150 Finland

This paper proposes a mixed integer conic programming (MICP) model to find the optimal type, size, and place of distributed generators (DG) over a multistage planning horizon in radial distribution systems. The proposed planning framework focuses on the optimal siting and sizing of wind turbines, photovoltaic panels, gas turbines, and energy storage devices (ESD). Inherently, renewable energy sources and electricity demands are subject to uncertainty. To handle such probabilistic situations in decision-making, the MICP model is extended into a two-stage stochastic programming model. To obtain more practical results, annual historical data are used to generate the scenarios. For the sake of tractability, the k-means clustering technique is used to reduce the number of scenarios while keeping the correlation between the uncertain data. Due to convexity, the proposed MICP model guarantees to find the global optimal solution. To show the potential and performance of the proposed model a 69-bus radial distribution system under different conditions is dully studied and a sensitivity analysis is conducted. Results and comparisons approve its effectiveness and usefulness.

关键词： conic programming Distributed generation Energy storage Multistage distribution system planning Renewable energy sources Stochastic programming

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Distributionally Robust Chance-Constrained Generation Expansion Planning

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IEEE TRANSACTIONS ON POWER SYSTEMS 2020年第4期35卷 2888-2903页

作者： Pourahmadi, Farzaneh Kazempour, Jalal Ordoudis, Christos Pinson, Pierre Hosseini, Seyed Hamid Sharif Univ Technol Dept Elect Engn Tehran *** Iran Tech Univ Denmark Dept Elect Engn DK-2800 Lyngby Denmark

This article addresses a centralized generation expansion planning problem, accounting for both long- and short-term uncertainties. The long-term uncertainty (demand growth) is modeled via a set of scenarios, while the short-term uncertainty (wind power generation) is described by a family of probability distributions with the same first- and second-order moments obtained from historical data. The resulting model is a distributionally robust chance-constrained optimization problem, which selects the conventional generating units to be built among predefined discrete options. This model includes a detailed representation of unit commitment constraints. To achieve computational tractability, we use a tight relaxation approach to convexify unit commitment constraints and solve the model with linear decision rules, resulting in a mixed-integer second-order cone program. It is observed that the proposed model exhibits better out-of-sample performance in terms of total expected system cost and its standard deviation compared to a chance-constrained model that assumes a Gaussian distribution of short-term uncertainty. A similar observation is made when comparing the proposed model against a chance-constrained program that uses empirical renewable power generation data with unknown type of distribution, recasting as either a robust optimization or a stochastic program.

关键词： Uncertainty Planning Computational modeling Optimization Stochastic processes Probability distribution Power generation Distributionally robust chance-constrained optimization conic programming linear decision rules generation expansion planning out-of-sample analysis unit commitment

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conic Optimization for Quadratic Regression Under Sparse Noise

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JOURNAL OF MACHINE LEARNING RESEARCH 2020年第1期21卷 1-36页

作者： Molybog, Igor Madani, Ramtin Lavaei, Javad Univ Calif Berkeley Dept Ind Engn & Operat Res Berkeley CA 94720 USA Univ Texas Arlington Dept Elect Engn Arlington TX 76102 USA

This paper is concerned with the quadratic regression problem, where the goal is to find the unknown state (numerical parameters) of a system modeled by a set of equations that are quadratic in the state. We focus on the setting when a subset of equations of fixed cardinality is subject to errors of arbitrary magnitudes (potentially adversarial). We develop two methods to address this problem, which are both based on conic optimization and are able to accept any available prior knowledge on the solution as an input. We derive sufficient conditions for guaranteeing the correct recovery of the unknown state for each method and show that one method provides a better accuracy while the other one scales better to large-scale systems. The obtained conditions consist in bounds on the number of bad measurements each method can tolerate without producing a nonzero estimation error. In the case when no prior knowledge is available, we develop an iterative-based conic optimization technique. It is proved that the proposed methods allow up to half of the total number of measurements to be grossly *** efficacy of the developed methods is demonstrated in different case studies, including data analytics for a European power grid.

关键词： nonlinear regression conic programming bad data detection

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Stochastic second-order cone programming: Applications models

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APPLIED MATHEMATICAL MODELLING 2012年第10期36卷 5122-5134页

作者： Alzalg, Baha M. Washington State Univ Dept Math Pullman WA 99164 USA

Second-order cone programs are a class of convex optimization problems. We refer to them as deterministic second-order cone programs (DSCOPs) since data defining them are deterministic. In DSOCPs we minimize a linear objective function over the intersection of an affine set and a product of second-order (Lorentz) cones. Stochastic programs have been studied since 1950s as a tool for handling uncertainty in data defining classes of optimization problems such as linear and quadratic programs. Stochastic second-order cone programs (SSOCPs) with recourse is a class of optimization problems that defined to handle uncertainty in data defining DSOCPs. In this paper we describe four application models leading to SSOCPs. (C) 2011 Elsevier Inc. All rights reserved.

关键词： conic programming Stochastic programming Second-order cone programming Optimization models

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