共查询到20条相似文献,搜索用时 31 毫秒
1.
Tadeusz Antczak 《Journal of Mathematical Analysis and Applications》2006,315(2):555-567
An η-approximation approach introduced by Antczak [T. Antczak, A new method of solving nonlinear mathematical programming problems involving r-invex functions, J. Math. Anal. Appl. 311 (2005) 313-323] is used to obtain a solution Mond-Weir dual problems involving r-invex functions. η-Approximated Mond-Weir dual problems are introduced for the η-approximated optimization problem constructed in this method associated with the original nonlinear mathematical programming problem. By the help of η-approximated dual problems various duality results are established for the original mathematical programming problem and its original Mond-Weir duals. 相似文献
2.
Tadeusz Antczak 《Applied mathematics and computation》2011,217(15):6652-6662
A new exact penalty function method, called the l1 exact exponential penalty function method, is introduced. In this approach, the so-called the exponential penalized optimization problem with the l1 exact exponential penalty function is associated with the original optimization problem with both inequality and equality constraints. The l1 exact exponential penalty function method is used to solve nonconvex mathematical programming problems with r-invex functions (with respect to the same function η). The equivalence between sets of optimal solutions of the original mathematical programming problem and of its associated exponential penalized optimization problem is established under suitable r-invexity assumption. Also lower bounds on the penalty parameter are given, for which above these values, this result is true. 相似文献
3.
Tadeusz Antczak 《Journal of Mathematical Analysis and Applications》2003,286(1):187-206
Invexity of a function is generalized. The new class of nonconvex functions, called B-(p,r)-invex functions with respect to η and b, being introduced, includes many well-known classes of generalized invex functions as its subclasses. Some properties of the introduced class of B-(p,r)-invex functions with respect to η and b are studied. Further, mathematical programming problems involving B-(p,r)-invex functions with respect to η and b are considered. The equivalence between saddle points and optima, and different type duality theorems are established for this type of optimization problems. 相似文献
4.
Tadeusz Antczak 《Journal of Mathematical Analysis and Applications》2006,322(2):971-989
A new method is used for solving nonlinear multiobjective fractional programming problems having V-invex objective and constraint functions with respect to the same function η. In this approach, an equivalent vector programming problem is constructed by a modification of the objective fractional function in the original nonlinear multiobjective fractional problem. Furthermore, a modified Lagrange function is introduced for a constructed vector optimization problem. By the help of the modified Lagrange function, saddle point results are presented for the original nonlinear fractional programming problem with several ratios. Finally, a Mond-Weir type dual is associated, and weak, strong and converse duality results are established by using the introduced method with a modified function. To obtain these duality results between the original multiobjective fractional programming problem and its original Mond-Weir duals, a modified Mond-Weir vector dual problem with a modified objective function is constructed. 相似文献
5.
T. Antczak 《Journal of Optimization Theory and Applications》2007,132(1):71-87
In this paper, the η-approximation method introduced by Antczak (Ref. 1) for solving a nonlinear constrained mathematical
programming problem involving invex functions with respect to the same function η is extended. In this method, a so-called
η-approximated optimization problem associated with the original mathematical programming problems is constructed; moreover,
an η-saddle point and an η-Lagrange function are defined. By the help of the constructed η-approximated optimization problem,
saddle-point criteria are obtained for the original mathematical programming problem. The equivalence between an η-saddle
point of the η-Lagrangian of the associated η-approximated optimization problem and an optimal solution in the original mathematical
programming problem is established. 相似文献
6.
Tadeusz Antczak 《Applications of Mathematics》2009,54(5):433-445
A new approach for obtaining the second order sufficient conditions for non-linear mathematical programming problems which
makes use of second order derivative is presented. In the so-called second order η-approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that
involves a second order η-approximation of both the objective function and the constraint function constituting the original problem. The equivalence
between the nonlinear original mathematical programming problem and its associated second orderη-approximated optimization problem is established under second order invexity assumption imposed on the functions constituting
the original optimization problem. 相似文献
7.
Tadeusz Antczak 《Journal of Computational and Applied Mathematics》2011,235(17):4991-5000
In this paper, a new approximation method is introduced to characterize a so-called vector strict global minimizer of order 2 for a class of nonlinear differentiable multiobjective programming problems with (F,ρ)-convex functions of order 2. In this method, an equivalent vector optimization problem is constructed by a modification of both the objectives and the constraint functions in the original multiobjective programming problem at the given feasible point. In order to prove the equivalence between the original multiobjective programming problem and its associated F-approximated vector optimization problem, the suitable (F,ρ)-convexity of order 2 assumption is imposed on the functions constituting the considered vector optimization problem. 相似文献
8.
Tadeusz Antczak 《Numerical Functional Analysis & Optimization》2017,38(9):1125-1142
In this paper, we use the η-approximation method for a class of non-convex multiobjective variational problems with invex functionals. In this approach, for the considered multiobjective variational problem, the associated η-approximated multiobjective variational problem is constructed at the given feasible solution. The equivalence between (weakly) e?cient solutions in the original multiobjective variational problem and its associated η-approximated multiobjective variational problem is established under invexity hypotheses. 相似文献
9.
In this paper, we extend the class of E-convex sets, E-convex and E-quasiconvex functions introduced by [Youness, E.A., 1999. E-convex sets, E-convex functions and E-convex programming. Journal of Optimization Theory and Applications 102, 439–450], respectively by [Syau, Yu-Ru, Lee, E. Stanley, 2005. Some properties of E-convex functions. Applied Mathematics Letters 18, 1074–1080] to E-invex set, E-preinvex, E-prequasiinvex and corresponding local concepts. Some properties of these classes are studied. As an application of our results, we consider the nonlinear programming problem for which, we establish that, under mild conditions, a local minimum is a global minimum. 相似文献
10.
Optimality conditions are obtained for a nonlinear fractional multiobjective programming problem involving η-semidifferentiable functions. Also, a general dual is formulated and a duality result is proved using concepts of generalized ρ-semilocally type I-preinvex functions. 相似文献
11.
《European Journal of Operational Research》2006,173(1):47-58
A nonlinear programming problem is considered where the functions involved are η-semidifferentiable. Fritz John and Karush–Kuhn–Tucker types necessary optimality conditions are obtained. Moreover, a result concerning sufficiency of optimality conditions is given. Wolfe and Mond–Weir types duality results are formulated in terms of η-semidifferentials. The duality results are given using concepts of generalized semilocally B-preinvex functions. 相似文献
12.
Vasile Preda 《Journal of Mathematical Analysis and Applications》2003,288(2):365-382
Necessary and sufficient optimality conditions are obtained for a nonlinear fractional multiple objective programming problem involving η-semidifferentiable functions. Also, a general dual is formulated and duality results are proved using concepts of generalized semilocally preinvex functions. 相似文献
13.
Optimality and duality for nonsmooth multiobjective programming problems with V-r-invexity 总被引:1,自引:0,他引:1
Tadeusz Antczak 《Journal of Global Optimization》2009,45(2):319-334
In the paper, we consider a class of nonsmooth multiobjective programming problems in which involved functions are locally Lipschitz. A new concept of invexity for locally Lipschitz vector-valued functions is introduced, called V-r-invexity. The generalized Karush–Kuhn–Tuker necessary and sufficient optimality conditions are established and duality theorems are derived for nonsmooth multiobjective programming problems involving V-r-invex functions (with respect to the same function η). 相似文献
14.
Tadeusz Antczak 《Applied mathematics and computation》2011,217(23):9606-9624
Minimax programming problems involving locally Lipschitz (Φ, ρ)-invex functions are considered. The parametric and non-parametric necessary and sufficient optimality conditions for a class of nonsmooth minimax programming problems are obtained under nondifferentiable (Φ, ρ)-invexity assumption imposed on objective and constraint functions. When the sufficient conditions are utilized, parametric and non-parametric dual problems in the sense of Mond-Weir and Wolfe may be formulated and duality results are derived for the considered nonsmooth minimax programming problem. With the reference to the said functions we extend some results of optimality and duality for a larger class of nonsmooth minimax programming problems. 相似文献
15.
Most real-life decision-making activities require more than one objective to be considered. Therefore, several studies have been presented in the literature that use multiple objectives in decision models. In a mathematical programming context, the majority of these studies deal with two objective functions known as bicriteria optimization, while few of them consider more than two objective functions. In this study, a new algorithm is proposed to generate all nondominated solutions for multiobjective discrete optimization problems with any number of objective functions. In this algorithm, the search is managed over (p − 1)-dimensional rectangles where p represents the number of objectives in the problem and for each rectangle two-stage optimization problems are solved. The algorithm is motivated by the well-known ε-constraint scalarization and its contribution lies in the way rectangles are defined and tracked. The algorithm is compared with former studies on multiobjective knapsack and multiobjective assignment problem instances. The method is highly competitive in terms of solution time and the number of optimization models solved. 相似文献
16.
P. Mandal C. Nahak 《Applied mathematics and computation》2011,217(21):8141-8148
In this paper we introduce a new type of generalized invex function, called (p, r) − ρ − (η, θ)-invex function and study symmetric duality results under these assumptions. In our study the nonnegative orthants for the constraints are replaced by closed convex cones and their polars. We establish weak and strong duality theorems under (p, r) − ρ − (η, θ)-invexity assumptions for the symmetric dual problems. We also give many examples to justify our results. 相似文献
17.
This paper addresses the problem of robust H∞ control for a class of switched nonlinear cascade systems with parameter uncertainty using the multiple Lyapunov functions (MLFs) approach. Each subsystem under consideration is composed of two cascade-connected parts. The uncertain parameters are assumed to be in a known compact set and are allowed to enter the system nonlinearly. Based on the explicit construction of Lyapunov functions, which avoids solving the Hamilton-Jacobi equations, sufficient conditions for the solvability of the robust H∞ control problem are presented. As an application, the hybrid robust H∞ control problem for a class of uncertain non-switched nonlinear cascade systems is solved when no single continuous controller is effective. Finally, a numerical example is provided to demonstrate the feasibility of the proposed method. 相似文献
18.
Heng-you Lan Yi-shun CuiYu Fu 《Communications in Nonlinear Science & Numerical Simulation》2012,17(4):1844-1851
In this paper, we consider and study a class of general nonlinear operator inclusion couples involving (A, η, m)-resolvent operators and relaxed cocoercive type operators in Hilbert spaces. We also construct a new perturbed iterative algorithm framework with errors and investigate variational graph convergence analysis for this algorithm framework in the context of solving the nonlinear operator inclusion couple along with some results on the resolvent operator corresponding to (A, η, m)-maximal monotonicity. The obtained results improve and generalize some well known results in recent literatures. 相似文献
19.
20.
Sergei Kucherenko 《Discrete Applied Mathematics》2007,155(14):1837-1841
Determining the maximum number of D-dimensional spheres of radius r that can be adjacent to a central sphere of radius r is known as the Kissing Number Problem (KNP). The problem has been solved for two, three and very recently for four dimensions. We present two nonlinear (nonconvex) mathematical programming models for the solution of the KNP. We solve the problem by using two stochastic global optimization methods: a Multi Level Single Linkage algorithm and a Variable Neighbourhood Search. We obtain numerical results for two, three and four dimensions. 相似文献