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ENGINEERING REPORTS 2020年第6期2卷

作者： Mehta, Ridhima Jawaharlal Nehru Univ Sch Comp & Syst Sci New Mehrauli RdJNU Ring Rd New Delhi 110067 India

In this article, we propose and formulate a single-objective nonlinearly constrained programming problem with delay and capacity constraints. Specifically, we consider the utility resource allocation with the goal of maximizing the throughput amongst the multiple heterogeneous sessions in the network. Several numerical experiments for multiple topologies exhibit the performance and global convergence process of the proposed iterative algorithm. These network topologies are considered with distinct source-destination communication sessions to emphasize the traffic flow analysis and optimal rate allocation vectors. For this, we employ recursive quadratic programming method and Lagrangian multiplier approach to solve the proposed optimization problem. The presented numerical results are obtained using Octave simulation tool. The results obtained from implementation of numerical simulation demonstrate the robustness and convergence performance of the proposed optimization scheme to optimal solution within finite number of iterations. Finally, we employ various global measures of fairness including the entropy-based index, G's fairness index, linear product-based fairness index, and Bossaer's fairness index to assess the performance of the proposed resource allocation scheme.

关键词： fairness measure nonlinear constrained optimization optimal value function recursive quadratic programming

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Two-point mid-range approximation enhanced recursive quadratic programming method

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2005年第5期29卷 398-405页

作者： Magazinovic, G Univ Split Fac Elect Engn Mech Engn & Naval Architecture Split 21000 Croatia

This research represents an attempt to combine good convergence properties of recursive quadratic programming methods with the benefits of mid-range approximations, initially developed in the field of structural optimization. In this paper, an optimization method based on Arora and coworkers' PLBA (Pshenichny-Lim-Belegundu-Arora) algorithm is proposed in which, during the line search phase, cost and constraint functions are substituted by their two-point approximations using the Generalized Convex Approximation formulae of Chickermane and Gea. The results showed that the proposed optimization method preserves the reliability and accuracy of the recursive quadratic programming method while it might simultaneously reduce the computational effort for some problems. Therefore, the proposed optimization method may be taken as potentially suitable for general design optimization purposes.

关键词： approximation design optimization line search recursive quadratic programming

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Optimal pile arrangement for minimizing differential settlements in piled raft foundations

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COMPUTERS AND GEOTECHNICS 2001年第4期28卷 235-253页

作者： Kim, KN Lee, SH Kim, KS Chung, CK Kim, MM Lee, S CoreTech Co Ltd Seoul 150101 South Korea Seoul Natl Univ Dept Civil Engn Seoul 151742 South Korea

This paper presents an optimal pile arrangement scheme fur minimizing the differential settlements of piled raft foundations. A raft is modeled as a plate based on the Mindlin theory, and soil and piles are modeled as Winkler and coupled springs, respectively. The stiffness of piles is obtained by the approximate analytical method proposed by Randolph and Wroth, and the modulus of the subgrade reaction is adopted to evaluate the Winkler spring constant. The objective function for the optimization is defined as the squared L-2 function norm of the gradient vector of the defected surface of the raft for circumventing difficulties in using direct definition of the maximum differential settlement. The optimization is performed with respect to the locations of the plies, The recursive quadratic programming is adopted for optimization. The validity and effectiveness of the proposed method are demonstrated by three numerical examples. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： differential settlement piled raft foundation optimal pile arrangement optimization recursive quadratic programming

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New theoretical results on recursive quadratic programming algorithms

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1998年第2期97卷 435-454页

作者： Martinez, JM Santos, LT Univ Estadual Campinas IMECC Dept Math Appl Campinas SP Brazil

recursive quadratic programming is a family of techniques developed by Bartholomew-Biggs and other authors for solving nonlinear programming problems. The first-order optimality conditions for a local minimizer of the augmented Lagrangian are transformed into a nonlinear system where both primal and dual variables appear explicitly. The inner iteration of the algorithm is a Newton-like procedure that updates simultaneously primal variables and Lagrange multipliers. In this way, as observed by Could, the implementation of the Newton method becomes stable, in spite of the possibility of having large penalization parameters. In this paper, the inner iteration is analyzed from a different point of view. Namely, the size of the convergence region and the speed of convergence of the inner process are considered and it is shown that, in some sense, both are independent of the penalization parameter when an adequate version of the Newton method is used. In other words, classical Newton-like iterations are improved, not only in relation to stability of the linear algebra involved, but also with regard to the ovearll convergence of the nonlinear process. Some numerical experiments suggset that, in fact, practical efficiency of the methods is related to these theoretical results.

关键词： recursive quadratic programming penalty methods Newton method

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Robust recursive quadratic programming algorithm model with global and superlinear convergence properties

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1997年第3期92卷 543-579页

作者： Facchinei, F Associate Professor Dipartitmento di Informatica e Sistemistica Universita di Roma “La Sapienza” Roma Italy

A new, robust recursive quadratic programming algorithm model based on a continuously differentiable merit function is introduced. The algorithm is globally and superlinearly convergent, uses automatic rules for choosing the penalty parameter, and can efficiently cope with the possible inconsistency of the quadratic search subproblem. The properties of the algorithm are studied tinder weak a priori assumptions;in particular, the superlinear convergence rate is established without requiring strict complementarity. The behavior of the algorithm is also investigated in the case where not all of the assumptions are met. The focus of the paper is on theoretical issues;nevertheless, the analysis carried out and the solutions proposed pave the way to new and more robust RQP codes than those presently available.

关键词： recursive quadratic programming exact penalty functions nonlinear programming constrained optimization regularity conditions

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A NOTE ON A METHOD FOR CONSTRAINED OPTIMIZATION-BASED ON recursive quadratic-programming

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 1994年第3-4期51卷 173-180页

作者： CORRADI, G [a]Dipartimento di Matematica per le decisioni economiche Facolta'di Economia Via Del Castro Laurenziano 9 00161 Roma

We consider a method for constrained minimization based on recursive quadratic programming. In this note we suggest an alternative form to obtain a descent direction for the penalty function. Some computational result... 详细信息

关键词： CONSTRAINED OPTIMIZATION recursive quadratic programming

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recursive quadratic-programming ALGORITHM THAT USES AN EXACT AUGMENTED LAGRANGIAN FUNCTION

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1990年第2期67卷 227-245页

作者： LUCIDI, S 1. Istituto di Analisi dei Sistemi ed Informatica CNR Rome Italy

An algorithm for nonlinear programming problems with equality constraints is presented which is globally and superlinearly convergent. The algorithm employs a recursive quadratic programming scheme to obtain a search direction and uses a differentiable exact augmented Lagrangian as line search function to determine the steplength along this direction. It incorporates an automatic adjustment rule for the selection of the penalty parameter and avoids the need to evaluate second-order derivatives of the problem functions. Some numerical results are reported.

关键词： recursive quadratic programming exact augmented Lagrangians nonlinear programming constrained optimization

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AN RQP ALGORITHM USING A DIFFERENTIABLE EXACT PENALTY-FUNCTION FOR INEQUALITY CONSTRAINED PROBLEMS

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MATHEMATICAL programming 1992年第1期55卷 49-68页

作者： DIPILLO, G FACCHINEI, F GRIPPO, L 1. Dipartimento di Informatica e Sistemistica Università di Roma “La Sapienza” 00184 Rome Italy

In this paper we propose a recursive quadratic programming algorithm for nonlinear programming problems with inequality constraints that uses as merit function a differentiable exact penalty function. The algorithm incorporates an automatic adjustment rule for the selection of the penalty parameter and makes use of an Armijo-type line search procedure that avoids the need to evaluate second order derivatives of the problem functions. We prove that the algorithm possesses global and superlinear convergence properties. Numerical results are reported.

关键词： recursive quadratic programming EXACT PENALTY FUNCTIONS NONLINEAR programming CONSTRAINED OPTIMIZATION

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A recursive quadratic-programming ALGORITHM THAT USES DIFFERENTIABLE EXACT PENALTY-FUNCTIONS

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MATHEMATICAL programming 1986年第3期35卷 265-278页

作者： POWELL, MJD YUAN, Y 1.Department of Applied Mathematics and Theoretical Physics University of Cambridge Silver Street CB3 9EW Cambridge England

In this paper, a recursive quadratic programming algorithm for solving equality constrained optimization problems is proposed and studied. The line search functions used are approximations to Fletcher's differentiable exact penalty function. Global convergence and local superlinear convergence results are proved, and some numerical results are given.

关键词： Constrained optimization exact penalty functions global convergence line search functions recursive quadratic programming

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A DIRECT METHOD OF LINEARIZATION FOR CONTINUOUS MINIMAX PROBLEMS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1987年第2期55卷 271-287页

作者： KIWIEL, KC 1.Systems Research Institute Polish Academy of Sciences Warsaw Poland

We consider the problem of minimizing a nondifferentiable function that is the pointwise maximum over a compact family of continuously differentiable functions. We suppose that a certain convex approximation to the objective function can be evaluated. An iterative method is given which uses as successive search directions approximate solutions of semi-infinite quadratic programming problems calculated via a new generalized proximity algorithm. Inexact line searches ensure global convergence of the method to stationary points.

关键词： Nonlinear programming nondifferentiable optimization minimax problems semi-infinite programming recursive quadratic programming

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