The aggregate constraint homotopy method uses a single smoothing constraint instead of m-constraints to reduce the dimension of its homotopy map, and hence it is expected to be more efficient than the combined homotop...
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The aggregate constraint homotopy method uses a single smoothing constraint instead of m-constraints to reduce the dimension of its homotopy map, and hence it is expected to be more efficient than the combined homotopy interior point method when the number of constraints is very large. However, the gradient and Hessian of the aggregate constraint function are complicated combinations of gradients and Hessians of all constraint functions, and hence they are expensive to calculate when the number of constraint functions is very large. In order to improve the performance of the aggregate constraint homotopy method for solving nonlinear programming problems, with few variables and many nonlinear constraints, a flattened aggregate constraint homotopy method, that can save much computation of gradients and Hessians of constraint functions, is presented. Under some similar conditions for other homotopy methods, existence and convergence of a smooth homotopy path are proven. A numerical procedure is given to implement the proposed homotopy method, preliminary computational results show its performance, and it is also competitive with the state-of-the-art solver KNITRO for solving large-scale nonlinear optimization.
The present paper is devoted to the application of the space transformation techniques for solving nonlinear programming problems. By using surjective mapping the original constrained optimization problem is transform...
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The present paper is devoted to the application of the space transformation techniques for solving nonlinear programming problems. By using surjective mapping the original constrained optimization problem is transformed to a problem in a new space with only equality constraints. For the numerical solution of the latter problem the stable version of the gradient-projection and Newton's methods are used. After inverse transformation to the original space a family of numerical methods for solving optimization problems with equality and inequality constraints is obtained. The proposed algorithms are based on the numerical integration of the systems of ordinary differential equations. These algorithms do not require feasibility of starting and current points, but they preserve feasibility. As a result of space transformation the vector fields of differential equations are changed and additional terms are introduced which serve as a barrier preventing the trajectories from leaving the feasible set. A proof of convergence is given.
Interval-valued univex functions are introduced for differentiable programming problems. Optimality and duality results are derived for a class of generalized convex optimization problems with interval-valued univex f...
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Interval-valued univex functions are introduced for differentiable programming problems. Optimality and duality results are derived for a class of generalized convex optimization problems with interval-valued univex functions.
Firstly, definition and methods of reliability assignment are introduced in this paper. And the nonlinear programming based on Lagrange multipliers method is described briefly. Meanwhile the calculation principle and ...
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ISBN:
(纸本)9781479900305
Firstly, definition and methods of reliability assignment are introduced in this paper. And the nonlinear programming based on Lagrange multipliers method is described briefly. Meanwhile the calculation principle and mathematic model are proposed. Secondly, determining the reliability index is discussed in the paper, and the reliability block diagram and allocation model are given. Base on the discussion before and the fight control with longitudinal pitch motion, the feasibility of the nonlinear programming method is needed to verify. Lastly, the allocated system reliability is bigger than the predicted threshold reliability parameter, which verifies that the used allocation method is feasible and reasonable.
A framework for solving a class of nonlinear programming problems via the filter method is presented. The proposed technique first solve a sequence of quadratic programming subproblems via line search strategy and to ...
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A framework for solving a class of nonlinear programming problems via the filter method is presented. The proposed technique first solve a sequence of quadratic programming subproblems via line search strategy and to induce global convergence, trial points are accepted provided there is a sufficient decrease in the objective function or constraints violation function. In the event when the step size has reached a minimum threshold such that the trial iterate is rejected by the filter, the algorithm temporarily exits to a trust region based algorithm to generate iterates that approach the feasible region and also acceptable to the filter. Computational results on selected large scale CUTE problems on the prototype code fiILS are very encouraging and numerical performance with LOQO and SNOPT show that the algorithm is efficient and reliable.
A class of semistrictly G-preinvex functions and optimality in nonlinear programming are further discussed. Firstly, the relationships between semistrictly G-preinvex functions and G-preinvex functions are further dis...
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A class of semistrictly G-preinvex functions and optimality in nonlinear programming are further discussed. Firstly, the relationships between semistrictly G-preinvex functions and G-preinvex functions are further discussed. Then, two interesting properties of semistrictly G-preinvexity are given. Finally, two optimality results for nonlinear programming problems are obtained under the assumption of semistrict G-preinvexity. The obtained results are new and different from the corresponding ones in the literature. Some examples are given to illustrate our results.
In today's business environment, many fresh food companies have complex supply networks to distribute their products. For example, agricultural products are distributed through a multiechelon supply chain which in...
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In today's business environment, many fresh food companies have complex supply networks to distribute their products. For example, agricultural products are distributed through a multiechelon supply chain which includes agricultural association, agricultural produce marketing corporations (APMCs), markets, and so forth. In this paper a fresh produce supply network model is designed to determine the optimal service area for APMCs, the replenishment cycle time of APMCs, and the freshness-keeping effort, while maximizing the total profit. The objective is to address the integrated facility location, inventory allocation, and freshness-keeping effort problems. This paper develops an algorithm to solve the nonlinear problem, provides numerical analysis to illustrate the proposed solution procedure, and discusses the effects of various system parameters on the decisions and total profits. A real case of an agricultural product supply chain in Taiwan is used to verify the model. Results of this study can serve as a reference for business managers and administrators.
Mechanical positioning of wood blocks in a peeling machine can be considerably improved by means of electronics with respect to the peeled veneer recovery. An opto-electronic measurement system renders log shape descr...
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Mechanical positioning of wood blocks in a peeling machine can be considerably improved by means of electronics with respect to the peeled veneer recovery. An opto-electronic measurement system renders log shape describing data to be processed in a microcomputer. The form of data is described 10 the paper. A cost function determining the optimal position of the peeling axis and suitable for the real-time optimization is formulated. Searching of the optimal position is described as a nonlinear optimal problem. Further, a solution of the problem using nonlinear programming approach and realizable 10 the real-time conditions is presented in the paper. The economical effects of the optimization are analyzed.
To solve the problem of long logistics delivery time in supply chain, a Mixed Integer Non-linear Program (MINLP) model is built by using Mixed Integer nonlinear programming theory. Firstly, the General algebraic model...
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To solve the problem of long logistics delivery time in supply chain, a Mixed Integer Non-linear Program (MINLP) model is built by using Mixed Integer nonlinear programming theory. Firstly, the General algebraic modeling system (GAMS) is used to build the model to fully integrate each parameter of logistics transportation, the total distribution time of the supply chain network, the coverage radius of the logistics base, the number of users, the total capacity of the logistics base, the mode of railway and road transportation, the nonlinear programming model is built and solved by DICOPT solver in GAMS. The cost of logistics can be decreased, transportation time can be reduced, and the logistics system's operating efficiency can be increased in the long term with the help of this algorithm. The proper operation of the logistics system is critical in encouraging the supply chain circulation of various industries and has a direct impact on the society's economic development. The optimal logistics distribution plan with 5 logistics bases covered users of 18 and railway capacity of 2. With the same railway capacity and the same total budget, the larger the number of covered users, the greater the total distribution time increases, but the larger the total budget, the growth of the total distribution time slows down significantly. Experiments show that MINLP model can solve the problem of logistics-based layout optimization in nonlinear logistics management.
We introduce some approximate optimal solutions and a generalized augmented Lagrangian in nonlinear programming, establish dual function and dual problem based on the generalized augmented Lagrangian, obtain approxima...
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We introduce some approximate optimal solutions and a generalized augmented Lagrangian in nonlinear programming, establish dual function and dual problem based on the generalized augmented Lagrangian, obtain approximate KKT necessary optimality condition of the generalized augmented Lagrangian dual problem, prove that the approximate stationary points of generalized augmented Lagrangian problem converge to that of the original problem. Our results improve and generalize some known results. Copyright (C) 2007.
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