We investigate the problem of finding a common solution of a general system of variational inequalities, a variational inclusion, and a fixed-point problem of a strictly pseudocontractive mapping in a real Hilbert space. Motivated by Nadezhkina and Takahashi's hybrid-extragradient method, we propose and analyze new hybrid-extragradient iterative algorithm for finding a common solution. It is proven that three sequences generated by this algorithm converge strongly to the same common solution under very mild conditions. Based on this result, we also construct an iterative algorithm for finding a common fixed point of three mappings, such that one of these mappings is nonexpansive, and the other two mappings are strictly pseudocontractive mappings.

Under the condition that the values of mapping $F$ are evaluated approximately, we propose a proximal analytic center cutting plane algorithm for solving variational inequalities. It can be considered as an approximation of the earlier cutting plane method, and the conditions we impose on the corresponding mappings are more relaxed. The convergence analysis for the proposed algorithm is also given at the end of this paper.

This paper is devoted to metric subregularity of a kind of generalized constraint equations. In particular, in terms of coderivatives and normal cones, we provide some necessary and sufficient conditions for subsmooth generalized constraint equations to be metrically subregular and strongly metrically subregular in general Banach spaces and Asplund spaces, respectively.

In this paper, the structural characteristic of urban multimodal transport system is fully analyzed and then a two-tier network structure is proposed to describe such a system, in which the first-tier network is used to depict the traveller’s mode choice behaviour and the second-tier network is used to depict the vehicle routing when a certain mode has been selected. Subsequently, the generalized travel cost is formulated considering the properties of both traveller and transport mode. A new link impedance function is proposed, in which the interferences between different vehicle flows are taken into account. Simultaneously, the bi-equilibrium patterns for multimodal transport network are proposed by extending Wardrop principle. Correspondingly, a bi-level programming model is then presented to describe the bi-equilibrium based assignment for multi-class multimodal transport network. The solution algorithm is also given. Finally, a numerical example is provided to illustrate the model and algorithm.

For the extended mixed linear complementarity problem (EML CP), we first present the characterization of the solution set for the EMLCP. Based on this, its global error bound is also established under milder conditions. The results obtained in this paper can be taken as an extension for the classical linear complementarity problems.

The robust local regularity and controllability problem for the Takagi-Sugeno (TS) fuzzy descriptor systems is studied in this paper. Under the assumptions that the nominal TS fuzzy descriptor systems are locally regular and controllable, a sufficient criterion is proposed to preserve the assumed properties when the structured parameter uncertainties are added into the nominal TS fuzzy descriptor systems. The proposed sufficient criterion can provide the explicit relationship of the bounds on parameter uncertainties for preserving the assumed properties. An example is given to illustrate the application of the proposed sufficient condition.

Under the environment of fuzzy factors including the return of market, performance of product, and the demanding level of market, we use the method of dynamic programming and establish the model of investment decision, in technology innovation project of enterprise, based on the dynamic programming. Analysis of the influence caused by the changes of fuzzy uncertainty factors to technological innovation project investment of enterprise.

Based on the model of symmetric and asymmetric duopoly option game, this paper discusses the present value of profit flows and the sunk investment costs for the trapezoidal fuzzy number. It constructs the fuzzy expressions of the investment value and investment threshold of followers and leaders under fuzzy environment and conducts numerical analysis. This offers a kind of explanation to the investment strategies under fuzzy environment.

It is with a great significance to discuss the selection model of regional strategic emerging industry. First, the paper uses the fuzzy optimization theory to select the central industry of area as the regional strategic emerging industry and try to optimize the weight’s calculation in the multistage fuzzy comprehensive evaluation to get more accurate results. Then it will do a strategic emerging industrial inspection about the advantage and ecological related index based on a multiobjective programming model and the maximum entropy.

An iterative sequence for quasi-$\varphi$-asymptotically nonexpansive multivalued mapping for modifying Halpern's iterations is introduced. Under suitable conditions, some strong convergence theorems are proved. The results presented in the paper improve and extend the corresponding results in the work by Chang et al. 2011.

A class of $G$-semipreinvex functions, which are some generalizations of the semipreinvex functions, and the $G$-convex functions, is introduced. Examples are given to show their relations among $G$-semipreinvex functions, semipreinvex functions and $G$-convex functions. Some characterizations of $G$-semipreinvex functions are also obtained, and some optimality results are given for a class of $G$-semipreinvex functions. Ours results improve and generalize some known results.

The main goal of this paper is to present a minmax programming model for the optimal dispatch of Traffic and Patrol Police Service Platforms with single traffic congestion. The objective is to minimize the longest time of the dispatch for Traffic and Patrol Police Service Platforms. Some numerical experiments are carried out, and the optimal project is given.

Traffic network equilibrium problems with capacity constraints of arcs are studied. A (weak) vector equilibrium principle with vector-valued cost functions, which are different from the ones in the work of Lin (2010), and three kinds of parametric equilibrium flows are introduced. Some necessary and sufficient conditions for a (weak) vector equilibrium flow to be a parametric equilibrium flow are derived. Relationships between a parametric equilibrium flow and a solution of a scalar variational inequality problem are also discussed. Some examples are given to illustrate our results.

Based on the single-leg air cargo issues, we establish a dynamic programming model to consider the overbooking and space inventory control problem. We analyze the structure of optimal booking policy for every kind of booking requests and show that the optimal booking decision is of threshold type (known as booking limit policy). Our research provides a theoretical support for the air cargo space control.

We study some properties for parametric generalized vector equilibrium problems and the convergent behavior for the correspondent solution sets of this problem under some suitable conditions. Several existence results and the topological structures of the efficient solutions set are established. Some new results of existence for weak solutions and strong solutions are derived. Finally, we give some examples to illustrate our theory including the example studied by Fang (1992), who established the perturbed nonlinear program $(P_{\mu })$ and described successfully that the optimal solution of $(P_{\mu })$ will approach the optimal solution of linear program (P).

We consider the expected residual minimization method for a class of stochastic quasivariational inequality problems (SQVIP). The regularized gap function for quasivariational inequality problem (QVIP) is in general not differentiable. We first show that the regularized gap function is differentiable and convex for a class of QVIPs under some suitable conditions. Then, we reformulate SQVIP as a deterministic minimization problem that minimizes the expected residual of the regularized gap function and solve it by sample average approximation (SAA) method. Finally, we investigate the limiting behavior of the optimal solutions and stationary points.

A new hybrid projection algorithm is considered for a finite family of ${\lambda }_i$-strict pseudocontractions. Using the metric projection, some strong convergence theorems of common elements are obtained in a uniformly convex and 2-uniformly smooth Banach space. The results presented in this paper improve and extend the corresponding results of Matsushita and Takahshi, 2008, Kang and Wang, 2011, and many others.

We present a smooth augmented Lagrangian algorithm for semiinfinite programming (SIP). For this algorithm, we establish a perturbation theorem under mild conditions. As a corollary of the perturbation theorem, we obtain the global convergence result, that is, any accumulation point of the sequence generated by the algorithm is the solution of SIP. We get this global convergence result without any boundedness condition or coercive condition. Another corollary of the perturbation theorem shows that the perturbation function at zero point is lower semi-continuous if and only if the algorithm forces the sequence of objective function convergence to the optimal value of SIP. Finally, numerical results are given.

We first introduce a new notion of the partial and generalized cone subconvexlike set-valued map and give an equivalent characterization of the partial and generalized cone subconvexlike set-valued map in linear spaces. Secondly, a generalized alternative theorem of the partial and generalized cone subconvexlike set-valued map was presented. Finally, Kuhn-Tucker conditions of set-valued optimization problems were established in the sense of globally proper efficiency.

Suppose that $E$ is a real normed linear space, $C$ is a nonempty convex subset of $E$, $T:C\to C$ is a Lipschitzian mapping, and $x^{*}\in C$ is a fixed point of $T$. For given $x_0\in C$, suppose that the sequence $\{x_n\}\subset C$ is the Mann iterative sequence defined by $x_{n+1}=(1-{\alpha }_n)x_n+{\alpha }_{n}T{x}_n,n\ge 0$, where $\{{\alpha }_n\}$ is a sequence in [0, 1], , ${\sum }_{n=0}^{\infty }{\alpha }_n=\infty$. We prove that the sequence $\{x_n\}$ strongly converges to $x^{*}$ if and only if there exists a strictly increasing function $\mathrm{\Phi }:[0,\infty )\to [0,\infty )$ with $\mathrm{\Phi }(0)=0$ such that ${\mathrm{limsup}\hspace{0.17em}}_{n\to \infty }{\inf \hspace{0.17em}}_{j(x_n-x^{*})\in J(x_n-x^{*})}\{\langle T{x}_n-x^{*},j(x_n-x^{*})\rangle -\parallel x_n-x^{*}{\parallel }^2+\mathrm{\Phi }(\parallel x_n-x^{*}\parallel )\}\le 0$.

Sufficient optimality and sensitivity of a parameterized min-max programming with fixed feasible set are analyzed. Based on Clarke's subdifferential and Chaney's second-order directional derivative, sufficient optimality of the parameterized min-max programming is discussed first. Moreover, under a convex assumption on the objective function, a subdifferential computation formula of the marginal function is obtained. The assumptions are satisfied naturally for some application problems. Moreover, the formulae based on these assumptions are concise and convenient for algorithmic purpose to solve the applications.

Assume that F is a nonlinear operator which is Lipschitzian and strongly monotone on a nonempty closed convex subset C of a real Hilbert space H. Assume also that $\Omega$ is the intersection of the fixed point sets of a finite number of Lipschitzian pseudocontractive self-mappings on C. By combining hybrid steepest-descent method, Mann’s iteration method and projection method, we devise a hybrid iterative algorithm with perturbation F, which generates two sequences from an arbitrary initial point $x_0\in H$. These two sequences are shown to converge in norm to the same point $P_{\Omega }{x}_0$ under very mild assumptions.