In this paper, we use a generalized Fritz John condition to derive optimality conditions and duality results for a nonlinear programming with inequality constraints, under weak invexity with respect to different (eta(...
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In this paper, we use a generalized Fritz John condition to derive optimality conditions and duality results for a nonlinear programming with inequality constraints, under weak invexity with respect to different (eta(i))(i) assumption. The equivalence between saddle points and optima, and a characterization of optimal solutions are established under suitable generalized invexity requirements. Moreover, we prove weak, strong, converse and strict duality results for a Mond-Weir type dual. It is shown in this study, with examples, that the introduced generalized Fritz John condition combining with the invexity with respect to different (eta(i))(i) are especially easy in application and useful in the sense of sufficient optimality conditions and of characterization of solutions.
This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of p...
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This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear La- grange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. It is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Moreover, the paper develops the dual algorithm associ- ated with the proposed nonlinear Lagrangians. Numerical results reported suggest that the dual algorithm based on proposed nonlinear Lagrangians is effective for solving some nonlinear optimization problems.
In this paper we present a new trust-region SQP algorithm for nonlinear programming. This method avoids using a penalty function, nor a filter, and instead establishes a new step acceptance mechanism. Under some reaso...
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In this paper we present a new trust-region SQP algorithm for nonlinear programming. This method avoids using a penalty function, nor a filter, and instead establishes a new step acceptance mechanism. Under some reasonable assumptions, the method can be proved to be globally convergent to a KT point. Preliminary numerical experiments are presented that show the potential efficiency of the new approach. (C) 2014 Elsevier B.V. All rights reserved.
This paper is devoted to the study of tilt stability of local minimizers for classical nonlinear programs with equality and inequality constraints in finite dimensions described by twice continuously differentiable fu...
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This paper is devoted to the study of tilt stability of local minimizers for classical nonlinear programs with equality and inequality constraints in finite dimensions described by twice continuously differentiable functions. The importance of tilt stability has been well recognized from both theoretical and numerical perspectives of optimization, and this area of research has drawn much attention in the literature, especially in recent years. Based on advanced techniques of variational analysis and generalized differentiation, we derive here complete pointbased second-order characterizations of tilt-stable minimizers entirely in terms of the initial program data under the new qualification conditions, which are the weakest ones for the study of tilt stability.
A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter va...
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A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fr,chet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.
In this paper, we study augmented Lagrangian functions for nonlinear semidefinite programming (NSDP) problems with exactness properties. The term exact is used in the sense that the penalty parameter can be taken appr...
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This article deals with a new CAD system of railways routing. The route of railway as 3D curve is traditionally presented by two flat curves: plan and longitudinal profile. The plan of route is its projection on horiz...
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We explore properties of nonlinear programming problems (NLPs) that arise in the formulation of NMPC subproblems and show their influence on stability and robustness of NMPC. NLPs that satisfy linear independence cons...
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We explore properties of nonlinear programming problems (NLPs) that arise in the formulation of NMPC subproblems and show their influence on stability and robustness of NMPC. NLPs that satisfy linear independence constraint qualification (LICQ), second order sufficient conditions (SOSC) and strict complementarity (SC), have solutions that are continuous and differentiable with perturbations of the problem data. As a result, they are important prerequisites for nominal and ISS stability of NMPC controllers. Moreover, we show that ensuring these properties is possible through reformulation of the NLP subproblem for NMPC, through the addition of l1 penalty and barrier terms. We show how these properties also establish ISS of related sensitivity-based NMPC controllers, such as asNMPC and amsNMPC. Finally, we demonstrate the impact of our reformulated NLPs on several examples that have shown nonrobust performance on earlier NMPC strategies.
Supplier selection and inbound transport are among the main levers of the supply chain design and performance evaluation. Supplier selection decision is largely studied in the literature but little attention is given ...
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ISBN:
(纸本)9781467384803
Supplier selection and inbound transport are among the main levers of the supply chain design and performance evaluation. Supplier selection decision is largely studied in the literature but little attention is given to the transportation aspect in this decision. In this paper, a non-linear programming model is proposed to simultaneously determine the optimal number of suppliers to select and the order quantities to allocate to them, taking into account the transportation policies. The product bought from supplier can be shipped directly or via consolidation terminal to the buyer. Total logistics cost is the objective to minimize in the model, under suppliers, buyer and transportation constraints. A comprehensive example is provided to illustrate the model under some scenarios.
In this tutorial we discuss fundamental concepts that enable the solution of large-scale structured nonlinear programming problems on high-performance computers. We focus on linear algebra parallelization strategies a...
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ISBN:
(纸本)9781479978878
In this tutorial we discuss fundamental concepts that enable the solution of large-scale structured nonlinear programming problems on high-performance computers. We focus on linear algebra parallelization strategies and discuss how such strategies influence the choice of algorithmic frameworks capable of enforcing global convergence and deal with nonconvexities. We also discuss how the characteristics of different computing architectures influence the choice of algorithmic strategies.
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