Conditions are given for the viability and the weak convergence of an inexact, relaxed proximal point algorithm for finding a common zero of countably many cohypomonotone operators in a Hilbert space. In turn, new con...
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Conditions are given for the viability and the weak convergence of an inexact, relaxed proximal point algorithm for finding a common zero of countably many cohypomonotone operators in a Hilbert space. In turn, new convergence results are obtained for an extended version of the proximal method of multipliers in nonlinear programming.
A number of filled functions was proposed recently. This paper presents a new perspective of the filled functions: their barrier attribute. More filled functions can be constructed according to this new interpretation...
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A number of filled functions was proposed recently. This paper presents a new perspective of the filled functions: their barrier attribute. More filled functions can be constructed according to this new interpretation. Two of them are with finite barriers while the remains are with infinite barriers. (C) 2003 Elsevier Inc. All rights reserved.
The filled function method is an effective approach to find the global minimizer. Two of the recently proposed filled functions are L(X) and L-2(X). Having observed that the second term in L(X) or L-2(X) may result in...
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The filled function method is an effective approach to find the global minimizer. Two of the recently proposed filled functions are L(X) and L-2(X). Having observed that the second term in L(X) or L-2(X) may result in undesirable computational behaviors, in this paper we propose a new function L-3(X). Having also realized that the essence of the mitigation is to eliminate the discontinuity, we propose another new function L-4(X)Both theoretical analysis and numerical testing results are presented. (C) 2003 Elsevier Inc. All rights reserved.
Optimal power flow (OPF) is one of the main functions of power generation operation and control. It determines the optimal setting of generating units. It is therefore of great importance to solve this problem as quic...
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Optimal power flow (OPF) is one of the main functions of power generation operation and control. It determines the optimal setting of generating units. It is therefore of great importance to solve this problem as quickly and accurately as possible. This paper presents the solution of the OPF using genetic algorithm technique. This paper proposes a new methodology for solving OPF. This methodology is divided into two parts. The first part employs the genetic algorithm (GA) to obtain a feasible solution subject to desired load convergence, while the other part employs GA to obtain the optimal solution. The main goal of this paper is to verify the viability of using genetic algorithm to solve the OPF problem simultaneously composed by the load flow and the economic dispatch problem. Six buses system are used to highlight the goodness of this solution technique. (C) 2003 Elsevier Inc. All rights reserved.
Case-control studies are primary study designs used in genetic association studies. Sasieni (Biometrics 1997, 53, 1253-1261) pointed out that the allelic chi-square test used in genetic association studies is invalid ...
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Case-control studies are primary study designs used in genetic association studies. Sasieni (Biometrics 1997, 53, 1253-1261) pointed out that the allelic chi-square test used in genetic association studies is invalid when Hardy-Weinberg equilibrium (HWE) is violated in a combined population. It is important to know how much type I error rate is deviated from the nominal level under violated HWE. We examine bounds of type I error rate of the allelic chi-square test. We also investigate power of the goodness-of-fit test for HWE which can be used as a guideline for selecting an appropriate test between the allelic chi-square test and the modified allelic chi-square test, the latter of which was proposed for cases of violated HWE. In small samples, power is not large enough to detect the Wright's inbreeding model of small values of inbreeding coefficient. Therefore, when the null hypothesis of HWE is barely accepted, the modified test should be considered as an alternative method.
We consider the dynamic optimization of chemical processes with changes in the number of equilibrium phases. Recent work has shown that transitions in the number of phases can be modeled as a mathematical program with...
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We consider the dynamic optimization of chemical processes with changes in the number of equilibrium phases. Recent work has shown that transitions in the number of phases can be modeled as a mathematical program with equilibrium constraints (MPEC). This study generalizes the MPEC to consider dynamic characteristics. In particular, we describe a simultaneous discretization and solution strategy for dynamic optimization problems with complementarity constraints. These discretized problems are then solved with IPOPT-C, a recently developed barrier method for MPEC problems. Our approach is applied to two distillation examples. In the first, we consider the optimal startup of a binary batch distillation problem. In the second, we consider the dynamic operation of a cryogenic column for the separation of natural gas liquids. Both cases demonstrate the effectiveness of the approach on large scale MPEC problems. (C) 2004 Published by Elsevier Ltd.
Applications of nonlinear optimization problems with many degrees of freedom have become more common in the process industries, especially in the area of process operations. However, most widely used nonlinear program...
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Applications of nonlinear optimization problems with many degrees of freedom have become more common in the process industries, especially in the area of process operations. However, most widely used nonlinear programming (NLP) solvers are designed for the efficient solution of problems with few degrees of freedom. Here we consider a new NLP algorithm, IPOPT, designed for many degrees of freedom and many potentially active constraint sets. The IPOPT algorithm follows a primal-dual interior point approach, and its robustness, improved convergence, and computational speed compared to those of other popular NLP algorithms will be analyzed. To demonstrate its effectiveness on process applications, we consider large gasoline blending and data reconciliation problems, both of which contain nonlinear mass balance constraints and process properties. Results on this computational comparison show significant benefits from the IPOPT algorithm.
Conventional behavioral models such as Cournot to analyze generator behavior do not reflect many of the complexities of advanced electricity markets. Dispatch and pricing in a number of advanced pool-based electricity...
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Conventional behavioral models such as Cournot to analyze generator behavior do not reflect many of the complexities of advanced electricity markets. Dispatch and pricing in a number of advanced pool-based electricity markets worldwide explicitly recognize the co-optimization of ancillary services as well as transmission constraints. This paper discusses the development of, and experiments with, a multimarket Cournot model that deals with co-optimization of multiple commodities namely, energy and various classes of ancillary services and deals with transmission constraints that separate these commodity markets spatially. We also discuss the multimarket extension of the Cournot model to deal with bilateral contracts (for energy). A nonlinear programming formulation of the proposed model and the analysis of nodal prices are presented followed by a detailed set of experiments using a simple three-node system. The model is expected to add to understanding of complex interactions between energy and ancillary services markets, and further the impact transmission capacity limits may have on exercise of market power of each of these markets.
A general framework for a partial differential equation (PDE) model predictive control (MPC) problem is formulated. A first principle model of the system. described by a semi-linear PDE system with boundary control, i...
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A general framework for a partial differential equation (PDE) model predictive control (MPC) problem is formulated. A first principle model of the system. described by a semi-linear PDE system with boundary control, is employed in a model predictive control (MPC) framework. Here, the aim is to determine, off-line (i.e. without process measurement), the theoretical optimal behavior of the process that will be used during on-line MPC. Input and output constraints are handled in the optimization task using a nonlinear programming method. This strategy is evaluated for the optimization of processing temperatures during the manufacture of thick-sectioned polymer composite laminates. The off-line optimization task consists of determining the optimal temperature profile, otherwise known as the cure cycle. Moreover, for this particular process, the existence of a feasible constrained optimization problem is discussed through the design of a constraint bound. (C) 2003 Elsevier Ltd. All rights reserved.
Limit and shakedown theorems are exact theories of classical plasticity for the direct computation of the load-carrying capacity under constant and varying loads. Based on Melan's theorem, a solution procedure for...
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Limit and shakedown theorems are exact theories of classical plasticity for the direct computation of the load-carrying capacity under constant and varying loads. Based on Melan's theorem, a solution procedure for limit and shakedown analysis is established making use of symmetric Galerkin boundary element method (SGBEM) for two-dimensional (213) structures and traditional boundary element method (BEM) for three-dimensional (313) structures. The self-equilibrium stress fields are expressed by linear combination of several basic selfequilibrium stress fields with parameters to be determined. These basic self-equilibrium stress fields are elastic responses of the body to impose permanent strains obtained through elastic-plastic incremental analysis by SGBEM for 2D structures and by BEM for 3D structures, respectively. The Complex method is used to solve resulting non-linear programming directly and determine the maximal load amplifier. The numerical results show that it is efficient and accurate to solve limit and shakedown analysis problems by using the BEM and the Complex method. In this paper, the limit analysis is treated as a special case of shakedown analysis in which only proportional loading is considered. (C) 2003 Elsevier Ltd. All rights reserved.
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