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A multi-product continuous review inventory system with stochastic demand, backorders, and a budget constraint
, Article European Journal of Operational Research ; Volume 158, Issue 2 , 2004 , Pages 456-469 ; 03772217 (ISSN) ; Shultes, B. C ; Haji, R ; Sharif University of Technology
2004
Abstract
Common characteristics of inventory systems include uncertain demand and restrictions such as budgetary or storage space constraints. Several authors have examined budget constrained multi-item stochastic inventory systems controlled by continuous review policies without considering marginal shortage costs. Existing models assume that purchasing costs are paid at the time an order is placed, which is not always the case since in some systems purchasing costs are paid when orders arrive. In the latter case the maximum investment in inventory is random since the inventory level when an order arrives is a random variable. Hence payment of purchasing costs on delivery yields a stochastic budget...
Superlinearly Convergent Exact Penalty Methods with Projected Structured Secant Updates for Constrained Nonlinear Least Squares
, Article Journal of Optimization Theory and Applications ; Vol. 162, issue. 1 , 2014 , p. 154-190 ; Mahdavi-Amiri, N ; Sharif University of Technology
Abstract
We present a superlinearly convergent exact penalty method for solving constrained nonlinear least squares problems, in which the projected exact penalty Hessian is approximated by using a structured secant updating scheme. We give general conditions for the two-step superlinear convergence of the algorithm and prove that the projected structured Broyden-Fletcher-Goldfarb-Shanno (BFGS), Powell-symmetric-Broyden (PSB), and Davidon-Fletcher-Powell (DFP) update formulas satisfy these conditions. Then we extend the results to the projected structured convex Broyden family update formulas. Extensive testing results obtained by an implementation of our algorithms, as compared to the results...
Operations research and optimization (ORO)
, Article Optimization ; Volume 62, Issue 6 , Jan , 2013 , Pages 675-691 ; 02331934 (ISSN) ; Ansari, M. R ; Sharif University of Technology
2013
Abstract
We have recently proposed a structured algorithm for solving constrained nonlinear least-squares problems and established its local two-step Q-superlinear convergence rate. The approach is based on an earlier adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method. The structured adaptation makes use of the ideas of Nocedal and Overton for handling quasi-Newton updates of projected Hessians and adapts a structuring scheme due to Engels and Martinez. For robustness, we have employed a specific nonsmooth line search strategy, taking account of the least-squares objective. Numerical results also confirm the practical relevance of our special considerations for...
A two-step superlinearly convergent projected structured BFGS method for constrained nonlinear least squares
, Article Optimization ; Volume 62, Issue 6 , 2013 , Pages 797-815 ; 02331934 (ISSN) ; Mahdavi Amiri, N ; Sharif University of Technology
2013
Abstract
We present an exact penalty approach for solving constrained non-linear least-squares problems, when the projected structured Hessian is approximated by a projected version of the structured BFGS formula and prove its local two-step Q-superlinear convergence. The numerical results obtained in an extensive comparative testing experiment confirm the approach to be reliable and efficient
Superlinearly Convergent exact penalty projected structured Hessian updating Schemes for constrained nonlinear least squares: Asymptotic analysis
, Article Bulletin of the Iranian Mathematical Society ; Volume 38, Issue 3 , 2012 , Pages 767-786 ; 10186301 (ISSN) ; Ansari, M. R ; Sharif University of Technology
2012
Abstract
We present a structured algorithm for solving constrained nonlinear least squares problems, and establish its local two-step Q-superlinear convergence. The approach is based on an adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method of Coleman and Conn for nonlinearly constrained optimization problems. The structured adaptation also makes use of the ideas of Nocedal and Overton for handling quasi-Newton updates of projected Hessians. We discuss the comparative results of the testing of our programs and three nonlinear programming codes from KNITRO on some randomly generated test problems due to Bartels and Mahdavi-Amiri. The results indeed confirm the...
Implementation of the eXtended finite element method (X-FEM) in frictional contact problems
, Article MATERIALS PROCESSING AND DESIGN; Modeling, Simulation and Applications - NUMIFORM '07: 9th International Conference on Numerical Methods in Industrial Forming Processes, Porto, 17 June 2007 through 21 June 2007 ; Volume 908 , 2007 , Pages 1573-1578 ; 0094243X (ISSN) ; Anahid, M ; Yadegaran, I ; Nikbakht, M ; Sharif University of Technology
2007
Abstract
Numerical modeling of engineering contact problems is one of the most difficult and demanding tasks in computational mechanics. In this paper, the extended finite element method is employed to simulate the presence of discontinuities caused by frictional contact based on the penalty approach. The FEM approximation is enriched by applying additional terms to simulate the frictional behavior of contact between two bodies. The penalty method, which is one of the most commonly used techniques for contact problems, is used to model the penetration between two contacting boundaries and the normal contact force is related to the penetration by a penalty parameter. Finally, numerical examples are...
Meshless local petrov-galerkin (MLPG) method for incompressible viscous fluid flows
, Article 2006 2nd ASME Joint U.S.-European Fluids Engineering Summer Meeting, FEDSM 2006, Miami, FL, 17 July 2006 through 20 July 2006 ; Volume 2006 , 2006 ; 0791837831 (ISBN); 9780791837832 (ISBN) ; Sharif University of Technology
2006
Abstract
In this paper, the truly Meshless Local Petrov-Galerkin (MLPG) method is extended for computation of unsteady incompressible flows, governed by the Navier-Stokes equations (NSE), in vorticity-stream function formulation. The present method is a truly meshless method based only on a number of randomly located nodes. The formulation is based on two equations including stream function Poisson equation and vorticity advection-dispersion-reaction eq. (ADRE). The meshless method is based on a local weighted residual method with the Heaviside step function and quartic spline as the test functions respectively over a local subdomain. Moving Least Square approximation (MLS) is employed in shape...
A robust combined trust region-line search exact penalty projected structured scheme for constrained nonlinear least squares
, Article Optimization Methods and Software ; Volume 30, Issue 1 , 2015 , Pages 162-190 ; 10556788 (ISSN) ; Mahdavi Amiri, N ; Sharif University of Technology
Abstract
We present a combined trust region-line search structured algorithm for solving constrained nonlinear least-squares problems. The approach is based on adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method of Coleman and Conn for nonlinearly constrained optimization problems. The structured adaptation also makes use of the ideas of Nocedal and Overton for handling quasi-Newton updates of projected Hessians. For robustness, we propose a new penalty parameter updating strategy and a specific line search strategy within the trust region, taking account of the least-squares objective and special structured considerations for the approximate projected...
A Penalty Method for Nonlinear Integer Programming Problems
, M.Sc. Thesis Sharif University of Technology ; Mahdavi Amiri, Nezamoddin (Supervisor)
Abstract
We study the general nonlinear integer programming problem. We consider two general classes of this problem: nonlinear integer programming problem and mixed integer nonlinear programming problem (MINLP). We explain the basic concepts for solving these problems and describe common methods for solving them, including branch and bound, Benders decomposition and outer approximation. Furthermore, we introduce two methods based on using penalty methods. Penalty based methods, by using appropriate penalty functions, convert a general nonlinear integer programming problem into a sequence of nonlinear programming problems and these problems are solved by a global optimization algorithm. Computational...
A Line Search Exact Penalty Method Using Steering Rules
,
M.Sc. Thesis
Sharif University of Technology
;
Mahdavi-Amiri, Nezamoddin
(Supervisor)
Abstract
We explain a new penalty method recently introduced in the literature for solv-ing constrained optimization problems. In this method, the penalty parameter is adjusted dynamically at every iteration to ensure su?cient progress in linear feasi-bility. A trust region is used to assist in the determination of the penalty parameter, but not in the step computation. It is shown that the algorithm has global conver-gence. We implement the algorithm and test the program on a number of di?cult optimization problems. The numerical results con?rm the e?ectiveness of the algo-rithm
Modeling of large deformation - Large sliding contact via the penalty X-FEM technique
, Article Computational Materials Science ; Volume 48, Issue 3 , May , 2010 , Pages 471-480 ; 09270256 (ISSN) ; Taheri Mousavi, S.M ; Sharif University of Technology
2010
Abstract
In this paper, an extended finite element method is employed to simulate the presence of discontinuities caused by the contact surface. In X-FEM, the need for mesh adaption to interface is neglected and the process is accomplished by partitioning the domain with some triangular sub-elements whose Gauss points are used for integration of the elements. The modified level set technique and the Heaviside enrichment function are employed to approximate the discontinuous displacement field of elements located on the contact surface. The penalty method is used to impose the contact constraints and establish the non-penetration condition. An efficient numerical algorithm is employed to model the...
A three-dimensional mesh-free model for analyzing multi-phase flow in deforming porous media
, Article Meccanica ; Volume 51, Issue 3 , 2016 , Pages 517-536 ; 00256455 (ISSN) ; Pak, A ; Sharif University of Technology
Springer Netherlands
Abstract
Fully coupled flow-deformation analysis of deformable multiphase porous media saturated by several immiscible fluids has attracted the attention of researchers in widely different fields of engineering. This paper presents a new numerical tool to simulate the complicated process of two-phase fluid flow through deforming porous materials using a mesh-free technique, called element-free Galerkin (EFG) method. The numerical treatment of the governing partial differential equations involving the equilibrium and continuity equations of pore fluids is based on Galerkin’s weighted residual approach and employing the penalty method to introduce the essential boundary conditions into the weak forms....
Element free galerkin mesh-less method for fully coupled analysis of a consolidation process
, Article Scientia Iranica ; Volume 16, Issue 1 A , 2009 , Pages 65-77 ; 10263098 (ISSN) ; Pak, A ; Sharif University of Technology
2009
Abstract
A formulation of the Element Free Galerkin (EFG), one of the mesh-less methods, is developed for solving coupled problems and its validity for application to soil-water problems is examined through numerical analysis. The numerical approach is constructed to solve, two governing partial differential equations of equilibrium and the. continuity of pore water, simultaneously. Spatial variables in a weak form, the displacement increment and excess pore, water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used to create the discretization of the...
Some numerical issues using element-free galerkin mesh-less method for coupled hydro-mechanical problems
, Article International Journal for Numerical and Analytical Methods in Geomechanics ; Volume 33, Issue 7 , 2009 , Pages 915-938 ; 03639061 (ISSN) ; Soga, K ; Pak, A ; Sharif University of Technology
2009
Abstract
A new formulation of the element-free Galerkin (EFG) method is developed for solving coupled hydromechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the...
Dictionary learning with low mutual coherence constraint
, Article Neurocomputing ; Volume 407 , 2020 , Pages 163-174 ; Babaie Zadeh, M ; Sharif University of Technology
Elsevier B.V
2020
Abstract
This paper presents efficient algorithms for learning low-coherence dictionaries. First, a new algorithm based on proximal methods is proposed to solve the dictionary learning (DL) problem regularized with the mutual coherence of dictionary. This is unlike the previous approaches that solve a regularized problem where an approximate incoherence promoting term, instead of the mutual coherence, is used to encourage low-coherency. Then, a new solver is proposed for constrained low-coherence DL problem, i.e., a DL problem with an explicit constraint on the mutual coherence of the dictionary. As opposed to current methods, which follow a suboptimal two-step approach, the new algorithm directly...
Three-dimensional simulation of fully coupled hydro-mechanical behavior of saturated porous media using Element Free Galerkin (EFG) method
, Article Computers and Geotechnics ; Volume 46 , 2012 , Pages 75-83 ; 0266352X (ISSN) ; Pak, A ; Sharif University of Technology
2012
Abstract
Meshless methods are a relatively new type of numerical methods that have attracted the attention of many researchers over the past years. So far, a number of meshless methods have been developed and applied to solve problems in various fields of engineering, including solid mechanics and geotechnical problems. The Element-Free Galerkin (EFG) method is adopted in this study for solving the governing partial differential equations of equilibrium and continuity of pore fluid flow for numerical simulation of coupled hydro-mechanical problems. For this purpose, the weak form of the governing equations is derived by applying the weighted residual method and Galerkin technique. The penalty method...