CONTACT PROBLEMS AND DUAL VARIATIONAL INEQUALITY OF 2－D ELASTOPLASTIC BEAM THEORY

In Order to study the frictional contact problems of the elastoplastic beam theory,an extended two-dimensional beam model is established, and a second order nonlinear equilibrium problem with both internal and external complementarity conditions is proposed. The external complementarity condition provides the free boundary condition. while the internal complemententarity condition gives the interface of the elastic and plastic regions. We prove that this bicomplementarity problem is equivalent to a nonlinear variational inequality The dual variational inequality is also developed.It is shown that the dual variational inequality is much easier than the primalvariational problem. Application to limit analysis is illustrated.

Dual worth trade-off method and its application for solving multiple criteria decision making problems

To overcome the limitations of the traditional surrogate worth trade-off （SWT） method and solve the multiple criteria decision making problem more efficiently and interactively, a new method labeled dual worth tradeoff （DWT） method is proposed. The DWT method dynamically uses the duality theory related to the multiple criteria decision making problem and analytic hierarchy process technique to obtain the decision maker＇s solution preference information and finally find the satisfactory compromise solution of the decision maker. Through the interactive process between the analyst and the decision maker, trade-off information is solicited and treated properly, the representative subset of efficient solutions and the satisfactory solution to the problem are found. The implementation procedure for the DWT method is presented. The effectiveness and applicability of the DWT method are shown by a practical case study in the field of production scheduling.

A TRUST REGION ALGORITHM VIA BILEVEL LINEAR PROGRAMMING FOR SOLVING THE GENERAL MULTICOMMODITY MINIMAL COST FLOW PROBLEMS

This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programming and convex theory,the generalized directional derivative of the general multicommodity minimal cost flow problems is derived.The global convergence and superlinear convergence rate of the proposed algorithm are established under some mild conditions.

On the Dual of a Mixed H_2/l_1 Optimisation Problem

The general discrete-time Single-Input Single-Output （SISO） mixed H2/l1 control problem is considered in this paper. It is found that the existing results of duality theory cannot be directly applied to this infinite dimension optimisation problem. By means of two finite dimension approximate problems, to which duality theory can be applied, the dual of the mixed H2/l1 control problem is verified to be the limit of the duals of these two approximate problems.

New Method for American Options Pricing

A new method using nonlinear regression to approximate the option price based on approximate dynamic programming is proposed. As a result a representation of the American option price is obtained as a solution to the dual minimization problem. In addition, an available Q-value iteration algorithm in practice is given.

Financial Valuation of Segment-Specific Marketing Activities and Market Segment Development

By applying methods of investment appraisal, this paper offers a financial approach for determining the optimal level of segment-specific marketing activities and market development under the conditions of imperfect markets and uncertainty. Within the scope of marketing planning and controlling, the model is suited to optimizing an enterprise＇s market activities and taking interdependencies between market segments, production, and investments into account. Applying duality theory of linear programming allows for identifying the income determinants and deriving formulas for a correct valuation by using （corrected） net present values （NPVs）. Under certain conditions, they can also be used to easily evaluate and financially interpret the effects of parameter changes. The author uses sensitivity analysis to support these findings and to obtain more information on the effects of these determinants.

Duality Theorems on Multi-objective Programming of Generalized Functions

The form of a dual problem of Mond-Weir type for multi-objective programming problems of generalized functions is defined and theorems of the weak duality, direct duality and inverse duality are proven.

On the Monge–Kantorovich Mass Transfer Problem in Higher Dimensions

This paper mainly investigates the approximation of a global maximizer of the Monge–Kantorovich mass transfer problem in higher dimensions through the approach of nonlinear partial differential equations with Dirichlet boundary.Using an approximation mechanism,the primal maximization problem can be transformed into a sequence of minimization problems.By applying the systematic canonical duality theory,one is able to derive a sequence of analytic solutions for the minimization problems.In the final analysis,the convergence of the sequence to an analytical global maximizer of the primal Monge–Kantorovich problem will be demonstrated.

ASSET-LIABILITY MANAGEMENT UNDER BENCHMARK AND MEAN-VARIANCE CRITERIA IN A JUMP DIFFUSION MARKET

This paper investigates continuous-time asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. Specifically, the authors consider one risk-free asset, one risky asset and one liability, where the risky asset＇s price is governed by an exponential Levy process, the liability evolves according to a Levy process, and there exists a correlation between the risky asset and the liability. Two models are established. One is the benchmark model and the other is the mean-variance model. The benchmark model is solved by employing the stochastic dynamic programming and its results are extended to the mean-variance model by adopting the duality theory. Closed-form solutions of the two models are derived.

Cachazo-Svrcek-Witten rules for tree-level gluonic amplitudes revisited

We provide a new proof of Cachazo-Svrcek-Witten rules for tree-level gluonic amplitudes.As a key step,we explicitly demonstrate the cancellation of spurious poles originating from the maximally helicity violating vertices in these rules.To achieve this,we introduce specially-defined two-off-shell-line sub-amplitudes and examine their residues at spurious poles.

Quantification of Symmetry

Symmetry is conventionally described in a polarized manner that the system is either completely symmetric or completely asymmetric.Using group theoretical approach to overcome this dichotomous problem,we introduce the degree of symmetry(DoS) as a non-negative continuous number ranging from zero to unity.Do S is defined through an average of the fidelity deviations of Hamiltonian or quantum state over its transformation group G,and thus is computable by making use of the completeness relations of the irreducible representations of G.The monotonicity of Do S can effectively probe the extended group for accidental degeneracy while its multi-valued natures characterize some(spontaneous) symmetry breaking.