Search

The purpose of this paper is to study the characterization of the solution set for nonconvex semi-infinite programming problems related to tangential subdifferentials. We give a necessary optimalit...

In this paper, the Hausdorff quasi-upper and Hausdorff quasi-lower semicontinuity for set-valued mappings are introduced to derive the upper semicontinuity and lower semicontinuity of cone constrai...

In this paper, we extend the classic optimal research and development (R&D) investment model into the regime-switching environment. We formulate a robust model to obtain the maximal net value funct...

In this paper, we consider a stochastic general epidemic model with relapse, graded cure and nonlinear incidence rate. We show the existence and uniqueness of a global positive solution for the mod...

In this paper, we first obtain some results for the vectorial Ekeland variational principle with a W-distance, in which the final space is a real linear space not necessarily endowed with a topolog...

In this paper, we establish the upper semi-continuity, lower semi-continuity and compactness of relaxed minimal and minimal solution mappings for parametric set optimization problems, where the obj...

This paper considers the minimisation problem of an integral functional with an integrand and a mixed nonconvex control constraint under some suitable conditions. We minimise the integral functiona...

In this article, a projection-type method for mixed variational inequalities is proposed in Hilbert spaces. The proposed method has the following nice features: (i) The algorithm is well defined wh...

In this paper, we consider the robust mean variance optimization problem where the probability distribution of assets’ returns is multivariate normal and the uncertain mean and covariance are contr...

This article deals with a control system governed by a semilinear nonlocal fractional evolution inclusion with Clarke subdifferential and its optimal control. First we establish an existence theorem of the mild solution for the presented control system by applying the measure of noncompactness, a fixed point theorem of a condensing multivalued map and some properties of Clarke subdifferential. Moreover, under some mild conditions, we obtain a result on the existence of an optimal control to the presented control system. Finally, an example is provided to demonstrate the main results.

In this paper, a continuous-time robust mean variance model in the jump-diffusion financial market with an intractable claim is considered, in which the price processes of the assets not only are driven by the Brownian motion, but also have the Poisson jumps. By combining the martingale representation theorem and the quantile formulation method, an explicit closed-form solution of the robust mean-variance portfolio selection model is given under some suitable assumptions.

In this paper, some characterizations for the generalized l-B-well-posedness and the generalized u-B-well-posedness of set optimization problems are given. Moreover, the Hausdorff upper semi-continuity of l-minimal solution mapping and u-minimal solution mapping are established by assuming that the set optimization problem is l-H-well-posed and u-H-well-posed, respectively. Finally, the upper semi-continuity and the lower semi-continuity of solution mappings to parametric set optimization problems are investigated under some suitable conditions.

In this paper, a class of hemivariational inequality problems are introduced and studied on Hadamard manifolds. Using the properties of Clarke’s generalized directional derivative and Fan-KKM lemma, an existence theorem of solution in connection with the hemivariational inequality problem is obtained when the constraint set is bounded. By employing some coercivity conditions and the properties of Clarke’s generalized directional derivative, an existence result and the boundedness of the set of solutions for the underlying problem are investigated when the constraint set is unbounded. Moreover, a sufficient and necessary condition for ensuring the nonemptiness of the set of solutions concerned with the hemivariational inequality problem is also given.

In this paper, we establish the connectedness of the sets of Henig efficient solutions, globally efficient solutions, weak efficient solutions, superefficient solutions and efficient solutions for a class of generalized vector equilibrium problems without the assumptions of monotonicity and compactness.

In this paper, a convex optimization problem with cone constraint (for short, CPC) is introduced and studied on Hadamard manifolds. Some criteria and characterizations for the solution set to be a set of generalized global weak sharp minima, generalized local weak sharp minima and generalized bounded weak sharp minima for (CPC) are derived on Hadamard manifolds.

In this paper, a class of generalized evolution variational inequalities arising in quasistatic friction contact problem for viscoelastic materials is introduced and studied. Under some suitable assumptions, we obtain an existence and uniqueness theorem of the solution for the generalized evolution variational inequalities by using Banach’s fixed point theorem. Moreover, we study two numerical approximation schemes of the problem: semidiscrete scheme and fully discrete scheme. For both schemes, we prove the existence of the solution and derive the error estimations.

In this article, a new class of generalized f-projected dynamical systems is introduced and studied in Banach spaces. A global existence and uniqueness result of generalized f-projected dynamical system is proved, which generalizes the existence result of Xia and Vincent [Y.S. Xia and T.L. Vincent, On the stability of global projected dynamical systems, J. Optim. Theory Appl. 106 (2009), pp. 129–150]. The global convergence stability of the generalized f-projected dynamical system and the sensitivity result of solutions set with perturbations of the constraint sets are also obtained under some suitable conditions.

In this paper, we introduce and study a new class of differential quasi-variational inequalities in finite dimensional Euclidean spaces. First, we prove existence theorems for Caratheodory weak solutions of the differential quasi-variational inequalities under various conditions. Furthermore, we establish a convergence result on Euler time-dependent procedure for solving the initial-value differential set-valued variational inequalities.

Degree theory has been developed as a tool for checking the solution existence of nonlinear equations. Hu and Parageorgiou [S.C. Hu, N.S. Parageorgiou, Generalisation of Browders degree theory, Trans. Amer. Math. Soc. 347 (1995), pp. 233–259] generalized the results of Browder [F.E. Browder, Fixed point theory and nonlinear problems, Bull. Amer. Math. Soc. 9 (1983), pp. 1–39] on the degree theory to mappings of the form f + T + G, where f is a bounded and demicotinuous mapping of class (S)+ from a bounded open set in a reflexive Banach space X into its dual X*, T is a maximal monotone mapping with 0 ∈ T(0) from X into X*, and G is an u.s.c. compact set-valued mapping from X into X*. In this article we continue to generalize and extend the results of Browder on the degree theory to mappings of the form f + T + G. By enlarging the class of maximal monotone mappings and pseudo-monotone homotopies we obtain some new results of the degree theory for such mappings. As an application, an existence result of solu...

In this article, we propose an easily implementable algorithm method for solving mixed variational inequalities. The proposed method combines two strategies: inexact projected subgradient methods and regularization techniques. We prove that the sequence generated by the method is strongly convergent to a solution of the problem in Hilbert spaces, whenever it exists. The results presented in this article generalize and improve some recent results.

This article introduces a new concept of an exceptional family of elements for a generalized set-valued variational inequality in Banach spaces. By using this concept and the degree theory for the generalized set-valued variational inequality introduced by Wang and Huang [Zh.B. Wang and N.J. Huang, Degree theory for a generalized set-valued variational inequality with an application in Banach spaces, J. Glob. Optim. 49 (2011), pp. 343–357], some solvability results for the generalized set-valued variational inequality and its special cases are given in Banach spaces under suitable conditions.

In this article, constrained continuous and combinatorial vector optimization problems (VOPs) are considered in the setting of finite-dimensional Euclidean spaces. Equivalence results between constrained integer and continuous VOPs are established by virtue of that between a constrained VOP and its penalized problem. Finally, one of the established equivalences is applied to derive necessary optimality conditions for a constrained integer VOP.

In this paper, we develop a new mixed Mann iteration process to approximate the fixed points of mixed increasing operators in ordered Banach spaces and discuss the convergence analysis of the iterative sequences generated by the iteration process. As an application, we develop a new iterative method for solving a class of nonlinear integral equations.

The aim of this work was to study the solution maps in the vector homogeneous quasi-equilibrium problems. Here, we establish some sufficient and necessary conditions for upper semicontinuity of the solution maps in the vector homogeneous quasi-equilibrium problems. The results presented extend and improve the preceding results of Oetlli and Yen [Oetlli, W. and Yen, N.D., 1995, Continuity of the solution set of homogeneous equilibrium problems and linear complementarity problems. In: F. Giannessi and A. Maugeri (Eds) Variational Inequalities and Network Equilibrium Problems (New York: Plenum Press)].

In this article, we introduce a new class of iterative sequences with errors for approximating the common fixed point of a couple of quasi-contractive mappings and show the stability of the iterative procedures with errors in q-uniformly smooth Banach spaces. Our results extend, improve and unify the corresponding results of Agarwal, Cho, Li, Huang, Chidume, Osilike, Liu, and others.

Let X,Y be two Banach spaces, K⊆K be a nonempty set, C⊆Y be a pointed, closed, and convex cone, ϕ :K × K→Y and Φ :K×K×K→Y be two mappings. In this article, we consider the vector equilibrium problem: find x∈K such that for all y∈K, and the extended vector equilibrium problem: find x∈K such that for all y∈K. To study the above problems, we extend the classical (S)+-conditions to vectorial bifunctions. Under (S)+-conditions, we give some existence results for these two problems.

In this paper, we study the stability of the Mann and Ishikawa iterative processes with errors for the nonlinear equations of φ-strongly accretive type operators in arbitrary real Banach spaces. We also study the stability of the Mann and Ishikawa iterative processes with errors for the iterative approximation of fixed point of Lipschitzian and φ-hemicontractive operators in arbitrary real Banach spaces. †The second author was supported by '98 APEC Post-Doctor Fellowship (KOSEF) while he visited Gyeongsang National University and the third author wishes to acknowledge the financial support of the Korea Research Foundation Grant (KRF-99-005-D00003).

In this paper, we give some existence and uniquzness of periodic solution for fully nonlinear wave equation in the form where a, 6, c are all constants and F is a continuous function in R6.