共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper the Pareto efficiency of a uniformly convergent multiobjective optimization sequence is studied. We obtain some relation between the Pareto efficient solutions of a given multiobjective optimization problem and those of its uniformly convergent optimization sequence and also some relation between the weak Pareto efficient solutions of the same optimization problem and those of its uniformly convergent optimization sequence. Besides, under a compact convex assumption for constraints set and a certain convex assumption for both objective and constraint functions, we also get some sufficient and necessary conditions that the limit of solutions of a uniformly convergent multiobjective optimization sequence is the solution of a given multiobjective optimization problem. 相似文献
2.
In general normed spaces,we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior.We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function.Moreover,we provide necessary and suffcient conditions about the existence of weak(sharp) Pareto solutions. 相似文献
3.
Zhe Chen 《Journal of Global Optimization》2013,55(3):507-520
In this paper, we present a unified approach for studying convex composite multiobjective optimization problems via asymptotic analysis. We characterize the nonemptiness and compactness of the weak Pareto optimal solution sets for a convex composite multiobjective optimization problem. Then, we employ the obtained results to propose a class of proximal-type methods for solving the convex composite multiobjective optimization problem, and carry out their convergence analysis under some mild conditions. 相似文献
4.
M. Arana-Jiménez G. Ruiz-Garzón R. Osuna-Gómez B. Hernández-Jiménez 《Journal of Optimization Theory and Applications》2013,156(2):266-277
In this paper, we unify recent optimality results under directional derivatives by the introduction of new pseudoinvex classes of functions, in relation to the study of Pareto and weak Pareto solutions for nondifferentiable multiobjective programming problems. We prove that in order for feasible solutions satisfying Fritz John conditions to be Pareto or weak Pareto solutions, it is necessary and sufficient that the nondifferentiable multiobjective problem functions belong to these classes of functions, which is illustrated by an example. We also study the dual problem and establish weak, strong, and converse duality results. 相似文献
5.
Zhe Chen 《Applicable analysis》2013,92(12):2457-2467
In this article, we investigate the nonemptiness and compactness of the weak Pareto optimal solution set of a multiobjective optimization problem with functional constraints via asymptotic analysis. We then employ the obtained results to derive the necessary and sufficient conditions of the weak Pareto optimal solution set of a parametric multiobjective optimization problem. Our results improve and generalize some known results. 相似文献
6.
Do Van Luu 《Journal of Optimization Theory and Applications》2014,160(2):510-526
Based on the extended Ljusternik Theorem by Jiménez-Novo, necessary conditions for weak Pareto minimum of multiobjective programming problems involving inequality, equality and set constraints in terms of convexificators are established. Under assumptions on generalized convexity, necessary conditions for weak Pareto minimum become sufficient conditions. 相似文献
7.
In this paper, we present a proximal point algorithm for multicriteria optimization, by assuming an iterative process which uses a variable scalarization function. With respect to the convergence analysis, firstly we show that, for any sequence generated from our algorithm, each accumulation point is a Pareto critical point for the multiobjective function. A more significant novelty here is that our paper gets full convergence for quasi-convex functions. In the convex or pseudo-convex cases, we prove convergence to a weak Pareto optimal point. Another contribution is to consider a variant of our algorithm, obtaining the iterative step through an unconstrained subproblem. Then, we show that any sequence generated by this new algorithm attains a Pareto optimal point after a finite number of iterations under the assumption that the weak Pareto optimal set is weak sharp for the multiobjective problem. 相似文献
8.
Yun Tang 《Journal of Mathematical Analysis and Applications》1983,96(2):505-519
In this paper necessary conditions and sufficient conditions are obtained for efficient solutions of multiobjective functions (Pareto optimum) on a Banach space subject to a (possibly) infinite number of equality and inequality constraints. 相似文献
9.
Various type of optimal solutions of multiobjective optimization problems can be characterized by means of different cones.
Provided the partial objectives are convex, we derive necessary and sufficient geometrical optimality conditions for strongly
efficient and lexicographically optimal solutions by using the contingent, feasible and normal cones. Combining new results
with previously known ones, we derive two general schemes reflecting the structural properties and the interconnections of
five optimality principles: weak and proper Pareto optimality, efficiency and strong efficiency as well as lexicographic optimality. 相似文献
10.
《Optimization》2012,61(3):321-322
In this article we establish necessary conditions for local Pareto and weak minima of multiobjective programming problems involving inequality, equality and set constraints in Banach spaces in terms of convexificators. 相似文献
11.
Pareto optimality in multiobjective problems 总被引:2,自引:0,他引:2
Yair Censor 《Applied Mathematics and Optimization》1977,4(1):41-59
In this study, the optimization theory of Dubovitskii and Milyutin is extended to multiobjective optimization problems, producing new necessary conditions for local Pareto optima. Cones of directions of decrease, cones of feasible directions and a cone of tangent directions, as well as, a new cone of directions of nonincrease play an important role here. The dual cones to the cones of direction of decrease and to the cones of directions of nonincrease are characterized for convex functionals without differentiability, with the aid of their subdifferential, making the optimality theorems applicable. The theory is applied to vector mathematical programming, giving a generalized Fritz John theorem, and other applications are mentioned. It turns out that, under suitable convexity and regularity assumptions, the necessary conditions for local Pareto optima are also necessary and sufficient for global Pareto optimum. With the aid of the theory presented here, a result is obtained for the, so-called, scalarization problem of multiobjective optimization.The author's work in this area is now supported by NIH grants HL 18968 and HL 4664 and NCI contract NO1-CB-5386. 相似文献
12.
T.Q. Bao 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(3):1089-1103
In this paper, new necessary conditions for Pareto minimal points to sets and Pareto minimizers for constrained multiobjective optimization problems are established without the sequentially normal compactness property and the asymptotical compactness condition imposed on closed and convex ordering cones in Bao and Mordukhovich [10] and Durea and Dutta [5], respectively. Our approach is based on a version of the separation theorem for nonconvex sets and the subdifferentials of vector-valued and set-valued mappings. Furthermore, applications in mathematical finance and approximation theory are discussed. 相似文献
13.
This paper deals with approximate Pareto solutions in convex multiobjective optimization problems. We relate two approximate
Pareto efficiency concepts: one is already classic and the other is due to Helbig. We obtain Fritz John and Kuhn–Tucker type
necessary and sufficient conditions for Helbig’s approximate solutions. An application we deduce saddle-point theorems corresponding
to these solutions for two vector-valued Lagrangian functions. 相似文献
14.
In this paper we introduce and study enhanced notions of relative Pareto minimizers for constrained multiobjective problems
that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical
notions of Pareto and weak Pareto efficiency/minimality. Using advanced tools of variational analysis and generalized differentiation,
we establish the existence of relative Pareto minimizers for general multiobjective problems under a refined version of the
subdifferential Palais-Smale condition for set-valued mappings with values in partially ordered spaces and then derive necessary
optimality conditions for these minimizers (as well as for conventional efficient and weak efficient counterparts) that are
new in both finite-dimensional and infinite-dimensional settings. Our proofs are based on variational and extremal principles
of variational analysis; in particular, on new versions of the Ekeland variational principle and the subdifferential variational
principle for set-valued and single-valued mappings in infinite-dimensional spaces. 相似文献
15.
Mansoureh Alavi Hejazi Nooshin Movahedian 《Numerical Functional Analysis & Optimization》2018,39(1):11-37
In this paper, we study necessary optimality conditions for local Pareto and weak Pareto solutions of multiobjective problems involving inequality and equality constraints in terms of convexificators. We develop the enhanced Karush–Kuhn–Tucker conditions and introduce the associated pseudonormality and quasinormality conditions. We also introduce several other new constraint qualifications which entirely depend on the feasible set. Then a connecting link between these constraint qualifications is presented. Moreover, we provide several examples that clarify the interrelations between the different results that we have established. 相似文献
16.
We study a multiobjective variational problem on time scales. For this problem, necessary and sufficient conditions for weak
local Pareto optimality are given. We also prove a necessary optimality condition for the isoperimetric problem with multiple
constraints on time scales. 相似文献
17.
New results are established for multiobjective DC programs with infinite convex constraints (MOPIC) that are defined on Banach spaces (finite or infinite dimensional) with objectives given as the difference of convex functions. This class of problems can also be called multiobjective DC semi-infinite and infinite programs, where decision variables run over finite-dimensional and infinite-dimensional spaces, respectively. Such problems have not been studied as yet. Necessary and sufficient optimality conditions for the weak Pareto efficiency are introduced. Further, we seek a connection between multiobjective linear infinite programs and MOPIC. Both Wolfe and Mond-Weir dual problems are presented, and corresponding weak, strong, and strict converse duality theorems are derived for these two problems respectively. We also extend above results to multiobjective fractional DC programs with infinite convex constraints. The results obtained are new in both semi-infinite and infinite frameworks. 相似文献
18.
Jiawei Chen La Huang Shengjie Li 《Journal of Optimization Theory and Applications》2018,178(3):794-823
In this paper, we investigate the separations and optimality conditions for the optimal solution defined by the improvement set of a constrained multiobjective optimization problem. We introduce a vector-valued regular weak separation function and a scalar weak separation function via a nonlinear scalarization function defined in terms of an improvement set. The nonlinear separation between the image of the multiobjective optimization problem and an improvement set in the image space is established by the scalar weak separation function. Saddle point type optimality conditions for the optimal solution of the multiobjective optimization problem are established, respectively, by the nonlinear and linear separation methods. We also obtain the relationships between the optimal solution and approximate efficient solution of the multiobjective optimization problem. Finally, sufficient and necessary conditions for the (regular) linear separation between the approximate image of the multiobjective optimization problem and a convex cone are also presented. 相似文献
19.
Zhe Chen 《Computational Optimization and Applications》2011,49(1):179-192
In this paper, we consider an extend-valued nonsmooth multiobjective optimization problem of finding weak Pareto optimal solutions.
We propose a class of vector-valued generalized viscosity approximation method for solving the problem. Under some conditions,
we prove that any sequence generated by this method converges to a weak Pareto optimal solution of the multiobjective optimization
problem. 相似文献
20.
Hédy Attouch Guillaume Garrigos Xavier Goudou 《Journal of Mathematical Analysis and Applications》2015
In a general Hilbert framework, we consider continuous gradient-like dynamical systems for constrained multiobjective optimization involving nonsmooth convex objective functions. Based on the Yosida regularization of the subdifferential operators involved in the system, we obtain the existence of strong global trajectories. We prove a descent property for each objective function, and the convergence of trajectories to weak Pareto minima. This approach provides a dynamical endogenous weighting of the objective functions, a key property for applications in cooperative games, inverse problems, and numerical multiobjective optimization. 相似文献