LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly eff...
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We consider the solution of a recurrent sub–problem within both constrained and unconstrained nonlinear programming: namely the minimization of a quadratic function subject to linear constraints. This problem appears...
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This paper presents an integrated cross-resolution framework for the traffic system state identification (TSSI) problem by simultaneously considering traffic state estimation (TSE), traffic flow model parameter estima...
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This paper presents an integrated cross-resolution framework for the traffic system state identification (TSSI) problem by simultaneously considering traffic state estimation (TSE), traffic flow model parameter estimation (MPE), and queue profile estimation (QPE) on transportation networks using heterogeneous data sources. Systematically considering the three tasks, that is, TSE, MPE, and QPE, in an integrated modeling framework helps to fully utilize information from different components and takes advantage of larger solution spaces, which is expected to improve the reliability and accuracy of system identification results. However, potential inconsistencies between different modeling components are introduced at the same time and should be carefully dealt with to ensure model feasibility. To minimize such inconsistencies, a novel nonlinear programming model was developed to formulate the TSSI problem by considering traffic flow models and observations from different resolutions. At the macroscopic level, we used a fluid queue approximation to model the traffic system of interest. Based on the assumption of polynomial arrival and departure rates, critical system measures such as time-dependent delay, travel time, and queue length were analytically derived. At the mesoscopic level, with the adoption of continuous space-time distribution (CSTD) functions, a continuous traffic state representation scheme is introduced to model traffic flow variables such as traffic volume, speed, and density. CSTD functions maintain the differentiability of traffic state variables such that partial differential equations in traffic flow models can be comprehensively considered in the proposed framework. A computational graph is constructed to represent the nonlinear programming model in a sequential propagation structure, which is then solved using a forward-backward method. Extensive numerical experiments based on real-world and hypothetical datasets were designed to demonstrate the
In this paper, we consider the optimal operations of a thermal system for heat source and air conditioning system with a thermal storage tank using nonlinear programming. Firstly, we develop the mathematical model of ...
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In this paper, we consider the optimal operations of a thermal system for heat source and air conditioning system with a thermal storage tank using nonlinear programming. Firstly, we develop the mathematical model of the system components by applying the energy and mass balance principles. Secondly, the static balance of the system model is validated by the operational data. Thirdly, by applying the nonlinear programming method, IPOPT (Interior Point OPTimizer), to the mathematical model, we show the optimal operations of a thermal system under variable conditions of chilled water temperature, such as the number of person, heat generating equipment, outdoor and indoor air conditions. Finally, dynamic simulation results showed that, the variable set points of the chilled water temperature for thermal storage tank have an effect on reducing the running cost of a day. ? 2021 Elsevier Ltd. All rights reserved.
Numerical simulation of latent heat thermal energy storage (LHTES) systems plays a fundamental role in studying the physical process and guiding the engineering design. Discretization of the PDEs describing the nonlin...
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Numerical simulation of latent heat thermal energy storage (LHTES) systems plays a fundamental role in studying the physical process and guiding the engineering design. Discretization of the PDEs describing the nonlinear solidification/melting process of phase change materials (PCMs) leads to a large-scale complex dynamics system, where the system behavior depends on a set of parameters. In a design setting, repeated model evaluations are required over the set of parameters results in significant computational burden. In this paper, an explicit analytic solution was built for the propagation of the solidification front in a cylindrical coordinate. The analytic solution approach is further employed to develop a low computational reduced model (RM) as a module for a shell-and-tube based LHTES heat exchanger. The levelized Cost of Energy (LCOE) is used as a design metric and the RM model is used to apply system-level constraints in the nonlinear programming formulation that facilitates efficient global optimal design of the PCM properties, flow conditions and tube geometries. The use of LCOE as the design metric prevents over design of the heat transfer rate and also establishes a fair ground for evaluation of different thermal storage technologies and their integrated applications with other systems. Optimal results showed that a higher effectiveness results in a higher LCOE;the velocity of the HTF and the length of the channel are highly correlated with each other;both larger PCM latent energy and conductivity result in lower LCOE. (C) 2021 Elsevier Ltd. All rights reserved.
In this paper, using the upper bound shakedown theorem by means of the displacement finite element method and nonlinear programming, a numerical method is proposed to obtain the shakedown limit of strip footing under ...
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In this paper, using the upper bound shakedown theorem by means of the displacement finite element method and nonlinear programming, a numerical method is proposed to obtain the shakedown limit of strip footing under repeated loading. Shakedown analysis is a powerful method that provides the possibility to determine the shakedown limit of a structure. The shakedown limit of a structure under repeated loading is a load limit below which the structure is in the safe zone and its behaviour is elastic. For cohesive-frictional soil, the Mohr-Coulomb yield criterion is considered without any linearization. The role of the unit weight of the soil in the shakedown limit of a footing under repeated load is studied. Also, the effect of repeated load on the reduction of the bearing capacity of footing is investigated in several examples.
We propose a class of inexact secant methods in association with the line search filter technique for solving nonlinear equality constrained optimization. Compared with other filter methods that combine the line searc...
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We propose a class of inexact secant methods in association with the line search filter technique for solving nonlinear equality constrained optimization. Compared with other filter methods that combine the line search method applied in most large-scale optimization problems, the inexact line search filter algorithm is more flexible and realizable. In this paper, we focus on the analysis of the local superlinear convergence rate of the algorithms, while their global convergence properties can be obtained by making an analogy with our previous work. These methods have been implemented in a Matlab code, and detailed numerical results indicate that the proposed algorithms are efficient for 43 problems from the CUTEr test set.
Failure to satisfy Constraint Qualifications (CQs) leads to serious convergence difficulties for state-of-the-art nonlinear programming (NLP) solvers. Since this failure is often overlooked by practitioners, a strateg...
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Failure to satisfy Constraint Qualifications (CQs) leads to serious convergence difficulties for state-of-the-art nonlinear programming (NLP) solvers. Since this failure is often overlooked by practitioners, a strategy to enhance the robustness properties for problems without CQs is vital. Inspired by penalty merit functions and barrier-like strategies, we propose and implement a combination of both in Ipopt. This strategy has the advantage of consistently satisfying the Linear Independence Constraint Qualification (LICQ) for an augmented problem, readily enabling regular step computations within the interior-point framework. Additionally, an update rule inspired by the work of Byrd et al. (2012) is implemented, which provides a dynamic increase of the penalty parameter as stationary points are approached. Extensive test results show favorable performance and robustness increases for our l(1)-penalty strategies, when compared to the regular version of Ipopt. Moreover, a dynamic optimization problem with nonsmooth dynamics formulated as a Mathematical Program with Complementarity Constraints (MPCC) was solved in a single optimization stage without additional reformulation. Thus, this l(1)-strategy has proved useful for a broad class of degenerate NLPs. Copyright (C) 2020 The Authors.
In this paper, a parametric linearization approach for obtaining an approximate global optimum solution of nonlinear programming (N.L.P) problems is proposed. Especially when the objective and/or the constraints are n...
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ISBN:
(纸本)9783030212483;9783030212476
In this paper, a parametric linearization approach for obtaining an approximate global optimum solution of nonlinear programming (N.L.P) problems is proposed. Especially when the objective and/or the constraints are non-smooth functions, we define a global weak differentiation to make in a sense the non-smooth functions as a new smooth functions. This new definition for weak differentiation enables us to use practically the classic algorithms for non-smooth N.L.P problems. In our approach, we transfer the N.L.P problems to a sequence of linear programming problems defined on the special feasible regions. We prove that the proposed approach is convergent to the global optimum solution of the original N.L.P problem when the norm of the partitions of the feasible region of N.L.P tends to zero. Numerical examples indicate that the proposed approach is extremely robust, and may be used successfully to obtain the approximate solution of a wide range of nonlinear programming problems.
The preliminary design process of manned or unmanned aircraft includes aircraft performance in trim flight. In this paper, a trim algorithm for computing flight-states and control inputs in trim flight is implemented ...
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ISBN:
(数字)9781624105982
ISBN:
(纸本)9781624105982
The preliminary design process of manned or unmanned aircraft includes aircraft performance in trim flight. In this paper, a trim algorithm for computing flight-states and control inputs in trim flight is implemented using a nonlinear optimization method for the propeller-driven-electric-powered unmanned air vehicle (UAV) which is designed and manufactured at Flight Laboratory IIT Kanpur. The sequential quadratic programming method (SQP) is adopted to perform the numerical analysis in three flight regimes, namely: steady-straight-level flight (SSLF), level turn flight (LTF) and climb turn flight (CTF). Analytical validation of numerical results for bank angle in LTF adds the novelty to this work. Additionally, numerical analysis reveals the SQP method takes less computation time than compared to a gradient descent method.
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