In this paper,through the use of image space analysis,optimality conditions for a class of variational inequalities with cone constraints are *** virtue of the nonlinear scalarization function,known as the Gerstewitz ...
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In this paper,through the use of image space analysis,optimality conditions for a class of variational inequalities with cone constraints are *** virtue of the nonlinear scalarization function,known as the Gerstewitz function,three nonlinear weak separationfunctions,two nonlinear regular weak separationfunctions and a nonlinear strong separationfunction are *** to nonlinearseparationfunctions,some optimality conditions of the weak and strong alternative for variational inequalities with cone constraints are derived.
This paper focuses on the investigation of regularity conditions by virtue of the image space analysis, based on nonconvex separation. We consider a scalar constrained optimization problem and employ the Gerstewitz se...
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This paper focuses on the investigation of regularity conditions by virtue of the image space analysis, based on nonconvex separation. We consider a scalar constrained optimization problem and employ the Gerstewitz separationfunction, which is well known from scalarization of vector optimization problems to present and investigate a collection of nonlinear weak separationfunctions in connection with methods of image space analysis. With the separation theorems associated with the Gerstewitz function, some image regularity conditions which guarantee the existence of a weak separationfunction, conducting a regular separation, are studied. In addition, a Lagrange type function and a penalty function are constructed, while the existence of saddle points and exact penalty functions are established by means of the image regularity conditions.
In this paper, we employ the image space analysis to investigate a Ky Fan quasi-inequality with cone constraints. By means of the oriented distance function, a new nonlinear weak (regular) separationfunction is intro...
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In this paper, we employ the image space analysis to investigate a Ky Fan quasi-inequality with cone constraints. By means of the oriented distance function, a new nonlinear weak (regular) separationfunction is introduced. Some necessary and sufficient optimality conditions, especially, a saddle-point sufficient optimality condition for the Ky Fan quasi-inequality with cone constraints, are obtained. By virtue of the nonlinear regular weak separationfunction, a gap function for the Ky Fan quasi-inequality with cone constraints is obtained. Moreover, we get an error bound for the solution set of the Ky Fan quasi-inequality with respect to the gap function under strongly monotone assumptions.
In this paper, we employ the image space analysis to study constrained inverse vector variational inequalities. First, sufficient and necessary optimality conditions for constrained inverse vector variational inequali...
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In this paper, we employ the image space analysis to study constrained inverse vector variational inequalities. First, sufficient and necessary optimality conditions for constrained inverse vector variational inequalities are established by using multiobjective optimization. A continuous nonlinearfunction is also introduced based on the oriented distance function and projection operator. This function is proven to be a weak separationfunction and a regular weak separationfunction under different parameter sets. Then, two alternative theorems are established, which lead directly to sufficient and necessary optimality conditions of the inverse vector variational inequalities. This provides a partial answer to an open question posed in Chen et al. (J Optim Theory Appl 166:460-479, 2015).
This work is devoted to examining inverse vector variational inequalities with constraints by means of a prominent nonlinear scalarizing functional. We show that inverse vector variational inequalities are equivalent ...
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This work is devoted to examining inverse vector variational inequalities with constraints by means of a prominent nonlinear scalarizing functional. We show that inverse vector variational inequalities are equivalent to multiobjective optimization problems with a variable domination structure. Moreover, we introduce a nonlinearfunction based on a well-known nonlinear scalarization function. We show that this function is a weak separationfunction and a regular weak separationfunction under different parameter sets. Then two alternative theorems are established, which will provide the basis for characterizing efficient elements of inverse vector variational inequalities.
In this paper, we employ the image space analysis to investigate an inverse variational inequality (for short, IVI) with a cone constraint. By virtue of the nonlinear scalarization function commonly known as the Gerst...
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In this paper, we employ the image space analysis to investigate an inverse variational inequality (for short, IVI) with a cone constraint. By virtue of the nonlinear scalarization function commonly known as the Gerstewitz function, three nonlinear weak separationfunctions, two nonlinear regular weak separationfunctions and a nonlinear strong separationfunction are first introduced. Then, by these nonlinear separation functions, theorems of the weak and strong alternative and some optimality conditions for IVI with a cone constraint are derived without any convexity. In particular, a global saddle-point condition for a nonlinearfunction is investigated. It is shown that the existence of a saddle point is equivalent to a nonlinearseparation of two suitable subsets of the image space. Finally, two gap functions and an error bound for IVI with a cone constraint are obtained.
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