Bundle methods have been well studied in nonsmooth optimization. In most of the bundle methods developed thus far (traditional bundle methods), at least one quadratic programming subproblem needs to be solved in each ...
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Bundle methods have been well studied in nonsmooth optimization. In most of the bundle methods developed thus far (traditional bundle methods), at least one quadratic programming subproblem needs to be solved in each iteration. In this paper, a simple version of bundle method with linear programming is proposed. In each iteration, a cutting-plane model subject to a constraint constructed by an infinity norm is minimized. Without line search or trust region techniques, the convergence of the method can be shown. Additionally, the infinity norm in the constraint can be generalized to p-norm. Preliminary numerical experiments show the potential advantage of the proposed method for solving large scale problems.
Long-term planning to meet the growth of electricity demand in a country or region is a decision of strategic importance that should aim at maximizing the benefits provided and at minimizing negative impacts on the en...
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Long-term planning to meet the growth of electricity demand in a country or region is a decision of strategic importance that should aim at maximizing the benefits provided and at minimizing negative impacts on the environment and society. In this sense, the objective of this study is to develop a methodology to determine the most suitable electric energy matrix of a country, that is, the best combination for the use of electricity generation sources. Thus, a multiobjective linear programming model is proposed to calculate the amount of energy that must be generated by each source available in the country, considering its internal demand and capacity constraints. In addition, this article aims to present the results of a case study in Brazil in the determination of its electric energy matrix, considering the use of several sources of electricity generation. The methodology developed was applied for the years 2015, 2020 and 2030 and generated some important reflections when compared with the actual values and current practices. The proposed model proved to be a useful tool to assist in the analysis and planning of the use, and possible extension, of the generation capacity of each electric power source of a given country.
This paper aims at optimizing the energy management of a smart power plant composed of wind turbines coupled with a Lithium Ion storage device in order to fulfill a power production commitment to the utility grid. The...
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This paper aims at optimizing the energy management of a smart power plant composed of wind turbines coupled with a Lithium Ion storage device in order to fulfill a power production commitment to the utility grid. The application of this case study is typically related to islanded electric grids. Our work particularly investigates and compares two classes of energy management strategies for design purpose: a first capable of providing the global optimum of the power flow planning from a linear programming (LP) approach thanks to a priori knowledge of future events in the environment;a second, based on a classical control heuristic without any a priori knowledge on the future, applicable in real time. Beyond the future objectives in terms of system design (techno-economical sizing optimization), the comparison of both approaches also aims at improving the predefined heuristic from the analysis of the ideal reference provided by the global LP optimizer. In this scope, a linear power flow model of the power plant is developed in compliance with a LP solver (Cplex). A particular attention is paid to the techno-economic optimization including storage cost evaluation, commitment failure penalties and exploitation gains. Simulations and optimizations are carried out over one year in order to take variability and seasonal features of the wind potential into account. (C) 2018 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
We study a time homogeneous discrete composite-action Markov decision process (CMDP) which needs to make multiple decisions at each state. In this particular Markov decision process, the state variables are divided in...
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We study a time homogeneous discrete composite-action Markov decision process (CMDP) which needs to make multiple decisions at each state. In this particular Markov decision process, the state variables are divided into two separable sets and a two-dimensional composite action is chosen at each decision epoch. To solve a composite-action Markov decision process, we propose a novel linear programming model (Contracted linear programming Model, CLPM). We show that the CLPM model obtains the optimal state values of a CMDP process. We analyze and compare the number of variables and constraints of the CLPM model and the Traditional linear programming Model (TLPM). Computational experiments compare running times and memory usage of the two models. The CLPM model outperforms the TLPM model in both time complexity and space complexity by theoretical analysis and computational experiments.
In recent years, cloud computing has emerged as the most popular technologies for accessing and delivering enterprise applications as the services to the end users over the Internet. Since different enterprises may of...
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In recent years, cloud computing has emerged as the most popular technologies for accessing and delivering enterprise applications as the services to the end users over the Internet. Since different enterprises may offer web services with various capabilities, these web services can be combined with other to provide the complete functionality of a large software application to meet the users' requests. Therefore, the service composition as an NP-hard optimization problem to combine the distributed and heterogeneous web services is introduced as a challenging issue. In this work, we propose a linear programming approach to web service composition problem which is called LP-WSC' to select the most efficient service per request in a geographically distributed cloud environment for improving the quality-of-service criteria. Finally, we evaluate the effectiveness of our approach under three scenarios with varying the number of atomic services per set. The experimental results indicate that the proposed approach significantly reduces the cost of selection and composition of the services and also increases the availability of services and the reliability of the servers compared with the other approaches.
The dual-drive H-gantry is widely used for high-speed, high-precision Cartesian motion. Compared with the conventional rigid-linked design, the flexure-linked counterpart is able to prevent the damage of joints for it...
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The dual-drive H-gantry is widely used for high-speed, high-precision Cartesian motion. Compared with the conventional rigid-linked design, the flexure-linked counterpart is able to prevent the damage of joints for its smaller interaxial coupling force. However, there are still barriers to further push up its precision, such as parametric uncertainties due to the inaccurate dynamical model, the possible induced vibration during high-speed motion, and the decentralized control structure required by industries. To maintain the tracking precision of carriages and minimize the vibration of the end effector, we aim to optimize parameters in decentralized controllers with choices of flexure pieces. We find that such decentralized feedback structure yields some uncontrollable but stabilizable states in the closed-loop system, and no direct solution from solving the algebraic Riccati equation is available in this case. Such structural constraint, together with constraints due to stability requirement and model uncertainties facilitates us to formulate an H-2 guaranteed cost control problem within a projected convex domain. From here, efficient numerical procedures are developed to obtain the global optimum by iterative linear programming. The real-time experiment validates the optimality and the robustness of the proposed method.
We consider the problem of finding consistent upper price bounds and super replication strategies for exotic options, given the observation of call prices in the market. This field of research is called model-independ...
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We consider the problem of finding consistent upper price bounds and super replication strategies for exotic options, given the observation of call prices in the market. This field of research is called model-independent finance and has been introduced by Hobson (Finance Stoch 2(4):329-347, 1998). Here we use the link to mass transport problems. In contrast to existing literature we assume that the marginal distributions at the two time points we consider are discrete probability distributions. This has the advantage that the optimization problems reduce to linear programs and can be solved rather easily when assuming a general martingale Spence Mirrlees condition. We will prove the optimality of left-monotone transport plans under this assumption and provide an algorithm for its construction. Our proofs are simple and do not require much knowledge of probability theory. At the end we present an example to illustrate our approach.
This Letter presented a new-order optimal method for lowering the computational complexity of the traditional minimax design of digital finite impulse response (FIR) filter utilising linear programming (LP) in bandwid...
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This Letter presented a new-order optimal method for lowering the computational complexity of the traditional minimax design of digital finite impulse response (FIR) filter utilising linear programming (LP) in bandwidth interleaving digital-to-analogue converter (BI-DAC). In this order optimal method, a one-by-one increasing method was presented to optimise all of digital FIR subfilters' orders in BI-DAC so that these digital FIR subfilters' orders could be optimised to simultaneously satisfy all of given upper bounds of the distortion and aliasing errors. A design example was used to verify the effectiveness and low computational complexity of the presented low-complexity minimax design utilising LP, and the simulation results were well-pleasing.
We give a characterization result for the integrality gap of the natural linear programming relaxation for the vertex cover problem. We show that integrality gap of the standard linear programming relaxation for any g...
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We give a characterization result for the integrality gap of the natural linear programming relaxation for the vertex cover problem. We show that integrality gap of the standard linear programming relaxation for any graph G equals (2 - 2/chi(f)(G)) where chi(f)(G) denotes the fractional chromatic number of G. (C) 2019 Published by Elsevier B.V.
The London Plan, the Greater London Authority?s spatial development strategy for London, has defined Heathrow as an Opportunity Area ? an area with the capacity to support additional homes and jobs ? since 2004, but p...
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The London Plan, the Greater London Authority?s spatial development strategy for London, has defined Heathrow as an Opportunity Area ? an area with the capacity to support additional homes and jobs ? since 2004, but progress on developing the area has been minimal. Uncertainty around the expansion of Heathrow Airport appears to have adversely affected progress. Nevertheless, the most recent London Plan stipulates that the Heathrow Opportunity Area should accommodate 13,000 new homes and 11,000 new jobs. In this article, multiobjective linear programming is used to investigate whether these figures are achievable given constraints on land availability and land use mix. How land uses might best be assigned to maximise home, job and gross value added (GVA) creation within the Heathrow Opportunity Area is also explored. The main contributions are to provide independent scrutiny of London?s development strategy and to present a mathematical framework for land use allocation planning decisions in urban areas. Findings show that given 700 ha of available land, as indicated in the London Plan, home and job creation figures can be met. However, there is insufficient brownfield land to meet these targets, and development on Green Belt land would very likely be necessary. Strong land use allocations for the area are found to more heavily feature financial and professional services, other office-based businesses, and shops. Rather than presenting a single land use ?solution?, results are presented using a wide range of visualisations to illustrate key trade-offs between different goals, with the secondary aim of promoting multi-objective linear programming to planners as a valuable tool to support spatial decisions and policy making.
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