广义隐向量拟变分不等式解的存在性(英文)

本文研究一类广义隐式向量拟变分不等式问题,利用Fan-Kakutani不动点定理证明其解存在,推广了相关的文献中的结论.

Compliant landing of a trotting quadruped robot based on hybrid motion/force robust control

A compliant landing strategy for a trotting quadruped robot on unknown rough terrains based on contact force control is presented. Firstly, in order to lower the disturbance caused by the landing impact force, a landing phase is added between the swing phase and the stance phase, where the desired contact force is set as a small positive constant. Secondly, the joint torque optimization of the stance legs is formulated as a quadratic programming(QP) problem subject to equality and inequality/bound constraints. And a primal-dual dynamical system solver based on linear variational inequalities(LVI) is applied to solve this QP problem. Furthermore, based on the optimization results, a hybrid motion/force robust controller is designed to realize the tracking of the contact force, while the constraints of the stance feet landing angles are fulfilled simultaneously. Finally, the experiments are performed to validate the proposed methods.

Traffic assignment problem under tradable credit scheme in a bi-modal stochastic transportation network: A cumulative prospect theory approach

The traffic equilibrium assignment problem under tradable credit scheme(TCS) in a bi-modal stochastic transportation network is investigated in this paper. To describe traveler’s risk-taking behaviors under uncertainty, the cumulative prospect theory(CPT) is adopted. Travelers are assumed to choose the paths with the minimum perceived generalized path costs, consisting of time prospect value(PV) and monetary cost. At equilibrium with a given TCS, the endogenous reference points and credit price remain constant, and are consistent with the equilibrium flow pattern and the corresponding travel time distributions of road sub-network. To describe such an equilibrium state, the CPT-based stochastic user equilibrium(SUE) conditions can be formulated under TCS. An equivalent variational inequality(VI) model embedding a parameterized fixed point(FP) model is then established, with its properties analyzed theoretically. A heuristic solution algorithm is developed to solve the model, which contains two-layer iterations. The outer iteration is a bisection-based contraction method to find the equilibrium credit price, and the inner iteration is essentially the method of successive averages(MSA) to determine the corresponding CPT-based SUE network flow pattern. Numerical experiments are provided to validate the model and algorithm.

Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings

We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.

A PROXIMAL POINT ALGORITHM FOR A SYSTEM OF GENERALIZED MIXED VARIATIONAL INEQUALITIES

This paper introduces and considers a new system of generalized mixed variational inequal- ities in a Hilbert space, which includes many new and known systems of variational inequalities and generalized variational inequalities as special cases. By using the two concepts of η-subdifferential and η-proximal mappings of a proper function, the authors try to demonstrate that the system of generalized mixed variational inequalities is equivalence with a fixed point problem. By applying the equivalence, a new and innovative η-proximal point algorithm for finding approximate solutions of the system of generalized mixed variational inequalities will be suggested and analyzed. The authors also study the convergence analysis of the new iterative method under much weaker conditions. The results can be viewed as a refinement and improvement of the previously known results for variational inequalities.

A smoothing Newton method for mathematical programs constrained by parameterized quasi-variational inequalities

We consider a class of mathematical programs governed by parameterized quasi-variational inequalities(QVI).The necessary optimality conditions for the optimization problem with QVI constraints are reformulated as a system of nonsmooth equations under the linear independence constraint qualification and the strict slackness condition.A set of second order sufficient conditions for the mathematical program with parameterized QVI constraints are proposed,which are demonstrated to be sufficient for the second order growth condition.The strongly BD-regularity for the nonsmooth system of equations at a solution point is demonstrated under the second order sufficient conditions.The smoothing Newton method in Qi-Sun-Zhou [2000] is employed to solve this nonsmooth system and the quadratic convergence is guaranteed by the strongly BD-regularity.Numerical experiments are reported to show that the smoothing Newton method is very effective for solving this class of optimization problems.