On the critical damping in multi-degree-of-freedom systems

The concept of criticality in viscously damped multi-degree-of-freedom systems is discussed. A necessary and sufficient condition for critical damping is presented. The fundamental physical basis is the same as in Beskos and Boley [ASME J. Appl. Mech. 47 (1980) 627], but numerical convenience is enhanced.     

General symmetries in optimal control

In this paper we study general symmetries for optimal control problems making use of the geometric formulation proposed in [7]. This framework allows us to reduce the number of equations associated with optimal control problems with symmetry and compare the solutions of the original system with the solutions of the reduced one. The reconstruction of the optimal controls starting from the reduced problem is also explored.     

Inexact Interior-Point Method

In this paper, we introduce an inexact interior-point algorithm for a constrained system of equations. The formulation of the problem is quite general and includes nonlinear complementarity problems of various kinds. In our convergence theory, we interpret the inexact interior-point method as an inexact Newton method. This enables us to establish a global convergence theory for the proposed algorithm. Under the additional assumption of the invertibility of the Jacobian at the solution, the superlinear convergence of the iteration sequence is proved.     

YB叶片泵降噪途径的探讨

通过对ＹＢ型叶片泵的固体振动、液压冲击与脉动的噪声测定与分析，确定噪声源并探讨了对该类泵行之有效的降噪途径。文章对新颖的高次方程定子曲线特性进行了数学模拟，并确定其特征方程各系数，同时，文章又探讨了对减振槽的优化设计，以其最小压差、最低液压冲击作为目标函数，确定了减振槽最佳几何尺寸。     

Radiation damping in closed expanding universes

The dynamics of a coupled model (harmonic oscillator-relativistic scalar field) in Conformal Robertson-Walker (k = +1) spacetimes is investigated. The exact radiation-reaction equation of the source-including the retarded radiation terms due to the closed space geometry – is obtained and analyzed. A suitable family of Lyapunov functions is constructed to show that, if the spacetime expands monotonely, then the source's energy damps. A numerical simulation of this equation for expanding Universes, with and without Future Event Horizon, is performed.     

A Global Optimization Algorithm using Lagrangian Underestimates and the Interval Newton Method

Convex relaxations can be used to obtain lower bounds on the optimal objective function value of nonconvex quadratically constrained quadratic programs. However, for some problems, significantly better bounds can be obtained by minimizing the restricted Lagrangian function for a given estimate of the Lagrange multipliers. The difficulty in utilizing Lagrangian duality within a global optimization context is that the restricted Lagrangian is often nonconvex. Minimizing a convex underestimate of the restricted Lagrangian overcomes this difficulty and facilitates the use of Lagrangian duality within a global optimization framework. A branch-and-bound algorithm is presented that relies on these Lagrangian underestimates to provide lower bounds and on the interval Newton method to facilitate convergence in the neighborhood of the global solution. Computational results show that the algorithm compares favorably to the Reformulation–Linearization Technique for problems with a favorable structure.     

Geometric approach to Fletcher's ideal penalty function

In this note, we derive a geometric formulation of an ideal penalty function for equality constrained problems. This differentiable penalty function requires no parameter estimation or adjustment, has numerical conditioning similar to that of the target function from which it is constructed, and also has the desirable property that the strict second-order constrained minima of the target function are precisely those strict second-order unconstrained minima of the penalty function which satisfy the constraints. Such a penalty function can be used to establish termination properties for algorithms which avoid ill-conditioned steps. Numerical values for the penalty function and its derivatives can be calculated efficiently using automatic differentiation techniques.     

Numerical experience with a polyhedral-norm CDT trust-region algorithm

In this paper, we study a modification of the Celis-Dennis-Tapia trust-region subproblem, which is obtained by replacing thel ₂-norm with a polyhedral norm. The polyhedral norm Celis-Dennis-Tapia (CDT) subproblem can be solved using a standard quadratic programming code.We include computational results which compare the performance of the polyhedral-norm CDT trust-region algorithm with the performance of existing codes. The numerical results validate the effectiveness of the approach. These results show that there is not much loss of robustness or speed and suggest that the polyhedral-norm CDT algorithm may be a viable alternative. The topic merits further investigation.The first author was supported in part by the REDI foundation and State of Texas Award, Contract 1059 as Visiting Member of the Center for Research on Parallel Computation, Rice University, Houston, Texas, He thanks Rice University for the congenial scientific atmosphere provided. The second author was supported in part by the National Science Foundation, Cooperative Agreement CCR-88-09615, Air Force Office of Scientific Research Grant 89-0363, and Department of Energy Contract DEFG05-86-ER25017.     

Stabilization of linear systems with saturation: a Sylvester equation approach

A new methodology of the partial eigenstructure assignmentby state feedback via Sylvester equation is used to obtain asolution of the constrained regulator problem for linear continuous-timeand discrete-time systems by using the reduced-order technique.     

Unconstrained and constrained global optimization of polynomial functions in one variable

In Floudas and Visweswaran (1990), a new global optimization algorithm (GOP) was proposed for solving constrained nonconvex problems involving quadratic and polynomial functions in the objective function and/or constraints. In this paper, the application of this algorithm to the special case of polynomial functions of one variable is discussed. The special nature of polynomial functions enables considerable simplification of the GOP algorithm. The primal problem is shown to reduce to a simple function evaluation, while the relaxed dual problem is equivalent to the simultaneous solution of two linear equations in two variables. In addition, the one-to-one correspondence between the x and y variables in the problem enables the iterative improvement of the bounds used in the relaxed dual problem. The simplified approach is illustrated through a simple example that shows the significant improvement in the underestimating function obtained from the application of the modified algorithm. The application of the algorithm to several unconstrained and constrained polynomial function problems is demonstrated.