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Discrete-time optimal control (DTOC) problems are large-scale optimization problems with a dynamic structure. In previous work this structure has been exploited to provide very fast and eecient local procedures. Two examples are the diierential dynamic programming algorithm (DDP) and the stagewise Newton procedure { both require only O(N) operations per(More)
The feasibility problem for a system of linear inequalities can be converted into an unconstrained optimization problem using ideas from the ellipsoid method, which can be viewed as a very simple minimization technique for the resulting nonlinear function. Using more sophisticated algorithms, we develop and investigate more eecient methods, which lead to(More)
In this paper, we propose a modiied BFGS method and study the global and superlinear convergence properties of this method. We show that under certain circumstances this modiied BFGS method corrects the eigenvalues better than the BFGS does. Our numerical results support this claim and also indicate that the modiied BFGS method may be competitive with the(More)
PURPOSE To investigate the effects of mycophenolate mofetil (MMF) on proliferation and mucin-5AC (MUC5AC) mRNA expression of normal human conjunctival goblet cells (CGCs) in vitro and to understand mechanisms of MMF in treatment of dry eye syndrome at molecular level. METHODS Purified human CGCs were treated with a series of graded concentrations of MMF(More)
Image degradation by loss of higher spatial frequencies causes form-deprivation myopia (FDM) in humans and animals, and cyclical illumination (flicker) at certain frequencies may prevent FDM. The molecular mechanisms underlying FDM and its prevention by flicker are poorly known. To understand them better, we have identified proteins that differ in amount in(More)
In the paper of Liao and Todd 3] two weighted centers are introduced and used to design algorithms for solving systems of linear inequalities. The linear programming problems can be solved via the weighted centers of a sequence of linear inequalities formed by letting the objective be an extra constraint and increasing the lower bound corresponding to the(More)