This paper describes and analyzes an algorithmic framework for solving nonlinear programming problems in which strict complementarity conditions and constraint qualifications are not necessarily satisfied at a solutio...
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This paper describes and analyzes an algorithmic framework for solving nonlinear programming problems in which strict complementarity conditions and constraint qualifications are not necessarily satisfied at a solution. The framework is constructed from three main algorithmic ingredients. The first is any conventional method for nonlinear programming that produces estimates of the Lagrange multipliers at each iteration;the second is a technique for estimating the set of active constraint indices;the third is a stabilized Lagrange - Newton algorithm with rapid local convergence properties. Results concerning rapid local convergence and global convergence of the proposed framework are proved. The approach improves on existing approaches in that less restrictive assumptions are needed for convergence and/or the computational workload at each iteration is lower.
In the design of feedback control systems, modern techniques are often neglected in favor of the more classical trial and error techniques due to the difficulty of incorporating practical engineering constraints. This...
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In the present work, a hybrid beam element based on exact kinematics is developed, accounting for arbitrarily large displacements and rotations, as well as shear deformable cross sections. At selected quadrature point...
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The complexity of many decision problems may require the formulation of nonlinear models able to consider in a more realistic way its physical, chemical, economical, and biological properties. With modern sophisticati...
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ISBN:
(纸本)0889865264
The complexity of many decision problems may require the formulation of nonlinear models able to consider in a more realistic way its physical, chemical, economical, and biological properties. With modern sophistication of data measurements and structures, and computing capabilities, the models can represent real problems with less aggregation levels, improving their dimensions by larger number of variables and parameters submitted to more constraints to exhibit feasible solutions to practical problems. Models with dynamic structure as: (i) marine multi-species fishery management, and (ii) optimal electric energy short-term generation scheduling for complex hydro-thermal systems can be constructed. Coupled sets of discrete-time difference equations describe the interacting dynamics of natural resources and the environment, and optimal control theory can be applied to build model structure and to parameters estimation, but the increase in model complexities as nonlinearities, time delays, supplementary inequality constraints on the state and the control variables imply critical numerical difficulties. Reliable nonlinear programming numerical optimization methods can deal with these questions efficiently.
A variation of the Polak method of feasible directions for solving nonlinear programming problems is shown to be related to the Topkis and Veinott method of feasible directions. This new method is proven to converge t...
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A variation of the Polak method of feasible directions for solving nonlinear programming problems is shown to be related to the Topkis and Veinott method of feasible directions. This new method is proven to converge to a Fritz John point under rather weak assumptions. Finally, numerical results show that the method converges with fewer iterations than that of Polak with a proper choice of parameters.
Interval-parameter nonlinear programming (INP) is an extension of conventional nonlinear optimization methods for handling both nonlinearities and uncertainties. However, challenges exist in its solution method, leadi...
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Interval-parameter nonlinear programming (INP) is an extension of conventional nonlinear optimization methods for handling both nonlinearities and uncertainties. However, challenges exist in its solution method, leading to difficulties in obtaining a global optimum. In this study, a 0-1 piecewise approximation approach is provided for solving the INP, through integration with an interactive algorithm for interval-parameter optimization problems. Thus, the INP model can be transformed into two deterministic submodels that correspond to the lower and upper bounds of the objective-function value. By solving the two submodels, interval solutions can be obtained, which are used for generating a range of decision options. The developed method is applied to a case of long-term municipal solid waste (MSW) management planning. Not only uncertainties expressed as interval values but also nonlinearities in the objective function can be tackled. Moreover, economies of scale (EOS) effects on waste-management cost can also be reflected. The results obtained can be used for generating decision alternatives and thus help waste managers to identify desired policies for MSW management and planning. Compared with the conventional interval-parameter linear and quadratic programs, the developed INP can better reflect system-cost variations and generate more robust solutions.
作者：
Lee, J.IBM Corp
Div Res Thomas J Watson Res Ctr Yorktown Hts NY 10598 USA
We examine various aspects of modeling and solution via mixed-integer nonlinear programming (MINLP). MINLP has much to offer as a powerful modeling paradigm. Recently, significant advances have been made in MINLP solu...
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We examine various aspects of modeling and solution via mixed-integer nonlinear programming (MINLP). MINLP has much to offer as a powerful modeling paradigm. Recently, significant advances have been made in MINLP solution software. To fully realize the power of MINLP to solve complex business optimization problems, we need to develop knowledge and expertise concerning MINLP modeling and solution methods. Some of this can be drawn from conventional wisdom? of mixed-integer linear programming (MILP) and nonlinear programming (NLP), but theoretical and practical issues exist that are specific to MINLP. This paper discusses some of these, concentrating on an aspect of a classical facility location problem that is well-known in the MILP literature, although here we consider a nonlinear objective function.
We prove a new local convergence property of some primal-dual methods for solving nonlinear optimization problems. We consider a standard interior point approach, for which the complementarity conditions of the origin...
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We prove a new local convergence property of some primal-dual methods for solving nonlinear optimization problems. We consider a standard interior point approach, for which the complementarity conditions of the original primal-dual system are perturbed by a parameter driven to zero during the iterations. The sequence of iterates is generated by a linearization of the perturbed system and by applying the fraction to the boundary rule to maintain strict feasibility of the iterates with respect to the nonnegativity constraints. The analysis of the rate of convergence is carried out by considering an arbitrary sequence of perturbation parameters converging to zero. We first show that, once an iterate belongs to a neighbourhood of convergence of the Newton method applied to the original system, then the whole sequence of iterates converges to the solution. In addition, if the perturbation parameters converge to zero with a rate of convergence at most superlinear, then the sequence of iterates becomes asymptotically tangent to the central trajectory in a natural way. We give an example showing that this property can be false when the perturbation parameter goes to zero quadratically.
Semi-penalty function methods, which are proposed by Nie, are new approaches combining sequential quadratic programming (SQP) methods and sequential penalty quadratical programming (SlQP) approaches. But in some cases...
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Semi-penalty function methods, which are proposed by Nie, are new approaches combining sequential quadratic programming (SQP) methods and sequential penalty quadratical programming (SlQP) approaches. But in some cases, the subproblem may be inconsistent in Nie's method. Therefore, we aim to overcome the inconsistence in this paper. We regard some constraints, which is satisfied in some point, as constraints. Other constraints are acted as penalty term. The convergent results are obtained. Further, we extend our new semi-penalty method to augmented Lagrangian penalty approaches. (C) 2003 Elsevier Inc. All rights reserved.
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