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OPTIMAL CABLE PROFILE OF LV RADIAL DISTRIBUTORS - 2 mathematical-programming methods

PROCEEDINGS OF THE INSTITUTION OF ELECTRICAL ENGINEERS-LONDON 1976年第4期123卷 331-334页

作者： HINDI, KS BRAMELLER, A HAMAM, YM UNIV MANCHESTER INST SCI & TECHNOLDEPT ELECT ENGN & ELECTRM60 1QD MANCHESTERENGLAND AMER UNIV BEIRUT DEPT ELECT ENGN & ELECTRBEIRUTLEBANON

Two different methods for finding the optimal cable profile of tapered low-voltage multibranched distributors are presented. One method is for tapering between nodes assuming a change in cable size can occur anywhere within a branch, the other is for tapering at nodes where a change in cable size is allowed only from branch to branch. Both can be embedded in a general procedure for designing distribution networks. Also, both cater for interconnectors, existing branches and the cost of losses.

关键词： mathematical programming methods designing distribution networks Network and transmission line calculations distribution networks mathematical programming optimal cable profile low voltage radial distributors

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Integration of Hydrogen Systems in Petroleum. Refinery

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CHEMICAL AND BIOCHEMICAL ENGINEERING QUARTERLY 2016年第3期30卷 291-304页

作者： Matijasevic, Lj. Petric, M. Univ Zagreb Fac Chem Engn & Technol Marulicev Trg 19 Zagreb 10000 Croatia Pharmaceut Co PLIVA Hrvatska Doo Prilaz Baruna Filipov 25 Zagreb 10000 Croatia

Considering the importance of hydrogen in crude oil refming, it is necessary to ensure its most efficient use to satisfy refinery hydrogen requirements. Effective hydrogen management provides maximum utilization of hydrogen. The mass balance of streams containing hydrogen plays a key role in addressing the hydrogen-network optimization problem. The purpose of this work was to analyze the refinery hydrogen network, composed of hydrogen sources and sinks. Mass integration principles and techniques have been applied in the optimization of the refinery hydrogen network. The methodology of hydrogen network integration is presented in a case study of a local petroleum refinery. The main objectives are to provide different solutions for reducing the amount of hydrogen not properly used in the local refinery and which is mostly sent to the fuel system, as well as the operating costs. Hydrogen pinch analysis is applied for targeting the minimum hydrogen consumption of the hydrogen system. A superstfucture-based mathematical model of the hydrogen network is developed to minimize the total operating costs. The non-linear programming optimization problem is solved by using optimization software GAMS. An additional hydrogen purification unit is introduced in the existing hydrogen network and the effect on the overall network is investigated. Network design with two hydrogen purification units has proved to be an optimal solution, with respect to the chosen objective function. These analyses and their results can assist the refinery to reduce and improve the efficiency of hydrogen management. The analyses covered only the existing equipment without additional investment.

关键词： hydrogen distribution pinch analysis superstructure mathematical programming methods hydrogen network optimization

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A new regularization approach for numerical differentiation

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INVERSE PROBLEMS IN SCIENCE AND ENGINEERING 2020年第12期28卷 1747-1772页

作者： Nayak, Abinash Univ Alabama Birmingham Dept Math Univ Hall1402 10th Ave South Birmingham AL 35294 USA

It is well known that the problem of numerical differentiation is an ill-posed problem and one requires regularization methods to approximate the solution. The commonly practiced regularization methods are (external) parameter-based like Tikhonov regularization, which has certain inherent difficulties associated with them. In such scenarios, iterative regularization methods serve as an attractive alternative. In this paper, we propose a novel iterative regularization method where the minimizing functional does not contain the noisy data directly, but rather a smoothed or integrated version of it. The advantage, in addition to circumventing the use of noisy data directly, is that the sequence of functions constructed during the descent process tends to avoid overfitting, and hence, does not corrupt the recovery significantly. To demonstrate the effectiveness of our method we compare the numerical results obtained from our method with the numerical results obtained from certain standard regularization methods such as Tikhonov regularization, Total-variation, etc.

关键词： Numerical differentiation Newton-type methods mathematical programming methods optimization and variational techniques Volterra integral equations inverse problems Tikhonov regularization iterative regularization numerical analysis

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On the Fulfillment of the Complementary Approximate Karush-Kuhn-Tucker Conditions and Algorithmic Applications

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2023年第2期197卷 705-736页

作者： Prado, Renan W. Santos, Sandra A. Simoes, Lucas E. A. Univ Estadual Campinas Campinas SP Brazil

Focusing on smooth constrained optimization problems, and inspired by the complementary approximate Karush-Kuhn-Tucker (CAKKT) conditions, this work introduces the weighted complementary approximate Karush-Kuhn-Tucker (WCAKKT) conditions. They are shown to be verified by limit points generated not only by safeguarded augmented Lagrangian methods, but also by inexact restoration methods, inverse and logarithmic barrier methods, and a penalized algorithm for constrained nonsmooth optimization. Under the analyticity of the feasible set description, and resting upon a desingularization result, the new conditions are proved to be equivalent to the CAKKT conditions. The WCAKKT conditions capture the algebraic elements of the desingularization result needed to characterize CAKKT sequences using a weighted complementarity condition that asymptotically sums zero. Due to its generality and strength, the new condition may help to enlighten the practical performance of algorithms in generating CAKKT sequences.

关键词： Nonlinear programming Sequential optimality conditions mathematical programming methods

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Advances in designing and targeting of water systems involving regeneration/treatment units

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JOURNAL OF CLEANER PRODUCTION 2018年第Part1期197卷 1394-1407页

作者： Fan, Xiao-Yan Li, Ai-Hong Klemes, Jiri Jaromir Liu, Zhi-Yong Hebei Univ Technol Sch Chem Engn & Technol Tianjin 300130 Peoples R China Chengde Petr Coll Dept Chem Engn Chengde 067000 Hebei Peoples R China Brno Univ Technol VUT Brno Fac Mech Engn NETME Ctr SPILTech 2896 2 Brno 61669 Czech Republic

It is of great significance to introduce regeneration/treatment units into a water system. Regeneration units and treatment units are the same in function and application, but different in destination of the outlet streams. The outlet streams of the regeneration units will be reused/recycled in the water system. The outlet streams of the treatment units will be discharged to environment. This paper provides a review of the development in designing and targeting of continuous water systems involving regeneration/treatment units. The features of Pinch Analysis methods and mathematical programming methods are discussed for the integration of regeneration system, treatment system and total water system separately. For a water system involving regeneration unit, it is addressed that the system can be formed by adding one or more additional source(s), regenerated stream(s), into a water system involving reuse only. The contribution of Liu's group based on the above insight is outlined. Finally, this review offers a guide for future efforts in the integration of water systems involving regeneration/treatment. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Water system integration Regeneration reuse Regeneration recycling Distributed wastewater treatment Total water system Water Pinch Analysis mathematical programming methods

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Stochastic proximal gradient methods for nonconvex problems in Hilbert spaces

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2021年第3期78卷 705-740页

作者： Geiersbach, Caroline Scarinci, Teresa Weierstrass Inst Mohrenstr 39 D-10117 Berlin Germany Univ Aquila Dept Informat Engn Comp Sci & Math Via Vetoio Loc Coppito I-67010 Laquila Italy

For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives. This paper presents convergence results for the stochastic proximal gradient method applied to Hilbert spaces, motivated by optimization problems with partial differential equation (PDE) constraints with random inputs and coefficients. We study stochastic algorithms for nonconvex and nonsmooth problems, where the nonsmooth part is convex and the nonconvex part is the expectation, which is assumed to have a Lipschitz continuous gradient. The optimization variable is an element of a Hilbert space. We show almost sure convergence of strong limit points of the random sequence generated by the algorithm to stationary points. We demonstrate the stochastic proximal gradient algorithm on a tracking-type functional with a L-1-penalty term constrained by a semilinear PDE and box constraints, where input terms and coefficients are subject to uncertainty. We verify conditions for ensuring convergence of the algorithm and show a simulation.

关键词： Stochastic programming Nonsmooth and nonconvex optimization Differential inclusions mathematical programming methods Partial differential equations with randomness Optimal control problems involving partial differential equations

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DESIGN FOR VEHICLE CRASHWORTHINESS USING MULTIBODY DYNAMICS

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INTERNATIONAL JOURNAL OF VEHICLE DESIGN 1994年第6期15卷 563-577页

作者： DIAS, JP PEREIRA, MS IDMEC - Instituto de Mecanica - Instituto Superior Tecnico Lisboa Portugal

This paper describes a methodology for the sensitivity analysis and optimization of planar constrained mechanical systems. Direct differentiation methods and finite difference techniques have been used in the design sensitivity calculations. The optimization process is developed within the framework of mathematical programming techniques. The sensitivity equations were constructed symbolically, subsequently integrated in the dynamic analysis equations of motion and solved simultaneously. Some examples are solved to demonstrate the use of the methodology including a crashworthiness design problem, where a plastic hinge concept has been used to model plastic deformations of the vehicle structure during the impact.

关键词： CRASHWORTHINESS IMPACT OPTIMIZATION LARGE PLASTIC DEFORMATIONS mathematical programming methods MULTIBODY SYSTEMS DYNAMICS VEHICLE DESIGN

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