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Inequality-minimization with a given public budget

JOURNAL OF ECONOMIC INEQUALITY 2018年第4期16卷 607-629页

作者： Koenig, Johannes Schroeder, Carsten Free Univ Berlin Sch Business & Econ Berlin Germany DIW Berlin SOEP Berlin Germany

We solve the problem of a social planner who seeks to minimize inequality via transfers with a fixed public budget in a distribution of exogenously given incomes. The appropriate solution method depends on the objective function: If it is convex, it can be solved by an interior-point algorithm. If it is quasiconvex, the bisection method can be used. Using artificial and real-world data, we implement the procedures and show that the optimal transfer scheme need not comply with a transfer scheme that perfectly equalizes incomes at the bottom of the distribution.

关键词： Redistribution Public transfers Inequality Optimization methods interior-point algorithm Bisection method

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interior-point algorithm FOR SHAKEDOWN ANALYSIS ACCOUNTING FOR LIMITED KINEMATICAL HARDENING

INTERIOR-POINT ALGORITHM FOR SHAKEDOWN ANALYSIS ACCOUNTING F...

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11th International Conference on Computational Plasticity (COMPLAS) - Fundamentals and Applications

作者： Simon, Jaan-W. Weichert, Dieter Rhein Westfal TH Aachen Inst Gen Mech D-52062 Aachen Germany

ISBN: (纸本)9788489925731

We present a numerical method for the computation of shakedown loads of structures under thermo-mechanical loading accounting for limited kinematical hardening. The method is based on the lower bound approach by Melan extended to the hardening using a two-surface model. Both the yield and the bounding surface are defined by the von Mises condition. Melan's shakedown theorem leads to a nonlinear convex optimization problem. This is solved by the interior-point algorithm ipsa recently developed by the authors. In this paper, theoretical and numerical aspects will be presented as well as numerical examples from mechanical engineering.

关键词： Shakedown Analysis Direct Methods interior-point algorithm Limited Kinematical Hardening Nonlinear Programming

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Preventive Security-Constrained DCOPF Formulation Using Power Transmission Distribution Factors and Line Outage Distribution Factors

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ENERGIES 2018年第6期11卷 1497页

作者： Hinojosa, Victor H. Gonzalez-Longatt, Francisco Univ Tecn Federico Santa Maria Dept Elect Engn Valparaiso 2390123 Chile Loughborough Univ Technol Sch Elect Elect & Syst Engn Loughborough LE11 3TU Leics England

This study proposes a very effective formulation to carry out the security-constrained direct current (DC)-based optimal power flow (OPF) problem using two linear factors: (i) the power transmission distribution factors (PTDF) and (ii) the line outage distribution factors (LODF). The security-constrained (SC) DCOPF problem has been reformulated using these linear distribution factors, and mainly the pre- and post-contingency constraints have been added into the optimization problem based on the active power unit generation (decision variables). The main advantage of this formulation is the reduction of decision variables as well as equality and inequality constraints. To validate the introduced formulation, several experiments have been conducted using MatPower, DIgSILENT Power Factory and Gurobi. Simulation results demonstrate both the feasibility to carry out the SCOPF problem and the potential applicability of the proposed formulation to medium and large-scale power systems.

关键词： DC optimal power flow power transfer distribution factors line outage distribution factors interior-point algorithm

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Creep constitutive models for viscoelastic materials based on fractional derivatives

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2017年第6期73卷 1377-1384页

作者： Xu, Huanying Jiang, Xiaoyun Shandong Univ Sch Math Jinan 250100 Peoples R China Shandong Univ Sch Math & Stat Weihai 264209 Peoples R China

To describe the time-dependent creep behavior of viscoelastic material, fractional constitutive relation models which are represented by the fractional element networks are studied. Three sets of creep experimental data for polymer and rock are employed to demonstrate the effectiveness of these fractional derivative models. The corresponding constrained problem of nonlinear optimization is solved with an interior-point algorithm to obtain best fitting parameters of these fractional derivative models. The comparison results of measured values and calculated values versus time are displayed through graphics. The results demonstrate that the fractional Poynting Thomson model is optimal in simulating the creep behavior of viscoelastic materials. And it also shows that the interior-point method is effective in the inverse problem to estimate parameters of fractional viscoelastic models. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Fractional viscoelastic models Viscoelastic material Poynting-Thomson model Parameter estimation interior-point algorithm

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A full-Newton step interior-point algorithm based on modified Newton direction

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OPERATIONS RESEARCH LETTERS 2011年第5期39卷 318-322页

作者： Zhang, Lipu Xu, Yinghong Zhejiang A&F Univ Dept Math Hangzhou 311300 Zhejiang Peoples R China Zhejiang Sci Tech Univ Dept Math Hangzhou 310018 Zhejiang Peoples R China

The central path plays a very important role in interior-point methods. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-point algorithm based on this search direction, the complexity bound of the algorithm is the best known for linear optimization. (C) 2011 Elsevier B.V. All rights reserved.

关键词： interior-point algorithm Full-Newton step Central path Complexity analysis

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MULTI-OBJECTIVE OPTIMISATION OF COMMUNITY BATTERY ENERGY STORAGE CAPACITY EXPLOITATION

MULTI-OBJECTIVE OPTIMISATION OF COMMUNITY BATTERY ENERGY STO...

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作者： Alizadeh, Marjan LAPPEENRANTA UNIVERSITY OF TECHNOLOGY

学位级别：硕士

Utilizing battery energy storage systems (BESS) in power systems can elevate the efficiency, reliability, stability and security of the system, and simultaneously can provide economic benefits for the battery operator. Profitability of allocating battery capacity to different electricity markets is a critical factor which should be evaluated precisely. Determining of the optimal battery capacity via an optimal bidding strategy for allocation to different electricity markets in Finland, i. e. Nord Pool day-ahead and intra-day markets and Fingrid frequency containment reserve markets is investigated in this thesis. The bidding model for the Nord Pool day-ahead and intra-day markets are developed as a stochastic profit maximization model. The optimization problem is formulated with the objective of maximizing the total expected value of battery system's profit subjected to various technical linear and non-linear constraints. Two Matlab® optimization algorithms are examined to solve the optimization problem effectively: interior-point algorithm and genetic algorithm. The optimization results indicate that employing the battery system in Elspot day-ahead and Elbas intraday markets is not profitable for battery owner due to high amount of battery costs. The capacity allocation of battery system to Fingrid frequency containment reserve markets for normal operation (FCR-N) and disturbances (FCR-D) are studied by applying two methods: optimization method and fixed power method. In the optimization method, an optimal model for battery system is formulated and solved by Matlab ®. The purpose of optimization is to maximize the profit with observing the market prices, battery costs, technical constraints of battery system and requirements of market. The optimization results show that the battery system is profitable in both FCR-N and FCR-D markets. In the fixed-power method a constant amount of battery power is supposed to be dedicated to Fingrid frequency markets for all hours

关键词： Battery Energy Storage System (BESS) battery capacity exploitation Finland electricity markets optimal bidding strategy techno-economic optimization interior-point algorithm genetic algorithm

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A full-step interior-point algorithm for linear complementarity problem based on a simple function

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JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES 2011年第6期32卷 1315-1332页

作者： Zhang, Lipu Xu, Yinghong Zhejiang A&F Univ Dept Math Zhejiang 311300 Peoples R China Shanghai Univ Dept Math Shanghai 200444 Peoples R China Zhejiang Sci Tech Univ Dept Math Zhejiang 310018 Peoples R China

In this paper, we design and analyze a new full-step interior-point algorithm for linear complementarity problem based on a very simple function. The algorithm uses the simple function to determine the searching direction and define the neighborhood of central path. The full-step used in the algorithm has local quadratic convergence property according to the proximity function which is also constructed by this simple function. We derive the iteration complexity for the algorithm and obtain the best-known iteration bounds for linear complementarity problem.

关键词： linear complementarity problems interior-point algorithm complexity analysis. 2000

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A starting-point strategy for interior-point algorithms for shakedown analysis of engineering structures

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ENGINEERING OPTIMIZATION 2014年第5期46卷 648-668页

作者： Simon, Jaan-Willem Hoewer, Daniel Weichert, Dieter Rhein Westfal TH Aachen Inst Appl Mech D-52074 Aachen Germany Rhein Westfal TH Aachen Inst Gen Mech D-52056 Aachen Germany

Lower-bound shakedown analysis leads to nonlinear convex optimization problems with large numbers of unknowns and constraints, the solution of which can be obtained efficiently by interior-point algorithms. The performance of these algorithms strongly depends on the choice of the starting point. In general, starting points should be located inside the feasible region. In addition, they should also be well centred. Although there exist several heuristics for the construction of suitable starting points, these are restricted, as long as only the mathematical procedure is considered without taking into account the nature of the underlying mechanical problem. Thus, in this article, a strategy is proposed for choosing appropriate starting points for interior-point algorithms applied to shakedown analysis. This strategy is based on both the mathematical characteristics and the physical meaning of the variables involved. The efficiency of the new method is illustrated by numerical examples from the field of power plant engineering.

关键词： starting point interior-point algorithm shakedown analysis large-scale problem

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Limit states of structures in n-dimensional loading spaces with limited kinematical hardening

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COMPUTERS & STRUCTURES 2015年第Jan.期147卷 4-13页

作者： Simon, Jaan-Willem Rhein Westfal TH Aachen Inst Appl Mech D-52074 Aachen Germany

The load bearing capacity of engineering structures subjected to varying thermo-mechanical loading can be determined most conveniently by shakedown analysis. Admittedly, if limited kinematical hardening is considered, shakedown analysis is, as yet, restricted to either one or two independently varying loads. In consequence, the aim of this paper is to extend existing formulations for arbitrary numbers of loading, which is inevitable for most technical applications. For this, limited kinematical hardening was incorporated into Melan's shakedown theorem by means of a two-surface model covering both alternating plasticity and ratcheting, generalized to n-dimensional loading spaces. As a result, the three-dimensional shakedown domain accounting for hardening is presented for a flanged pipe subjected to thermo-mechanical loading. (C) 2014 Civil-Comp Ltd and Elsevier Ltd. All rights reserved.

关键词： Shakedown analysis n-dimensional loading space Limited kinematical hardening interior-point algorithm Convex optimization Nonlinear programming

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First and second order derivatives for optimizing parallel RF excitation waveforms

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JOURNAL OF MAGNETIC RESONANCE 2015年 258卷 65-80页

作者： Majewski, Kurt Ritter, Dieter Siemens AG CT RTC BAM ORD DE D-80200 Munich Germany Siemens AG HC IM MR R&D SYS PHYS D-91050 Erlangen Germany

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Bloch equation Parallel transmit excitation Radio frequency pulse design Small tip angle interior-point algorithm Hessian matrix

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