Stochastic Linear-quadratic Control Problems with Affine Constraints

In this paper, we investigate the stochastic linear-quadratic control problems with affine constraints in random coefficients case. With the help of the Pontryagin maximum principle and stochastic Riccati equation, the dual problem of original problem is established and the feedback solution of the optimal control problem is obtained. Under the Slater condition, the equivalence is proved between the solutions to the original problem and the ones of the dual problem, and the KKT condition is also provided for the dual problem. Finally, an invertibility assumption is given for ensuring the uniqueness of the solutions to the dual problem

Inhibitive effect of triptolide on invasiveness of human fibrosarcoma cells by downregulating matrix metalloproteinase—9 expression

AbstractObjectiveTo explore the molecular mechanisms of antitumor properties of triptolide, a bioactive component isolated from the Chinese herb Tripterygium wolfordii Hook F.MethodsHuman fibrosarcoma HT-1080 cells were treated with different doses of triptolide for 72 h. Then the expression and activity of matrix metalloproteinase (MMP)-2 and -9 were measured and the invasiveness of triptolide-treated HT-1080 cells was compared with that of anti-MMP-9-treated HT-1080 cells.Results18 nmol/L triptolide inhibited the gene expression and activity of MMP-9, but not those of MMP-2, in HT-1080 cells. In addition, both 18 nmol/L triptolide and 3 μg/mL anti-MMP-9 significantly reduced the invasive potential of HT-1080 cells, by about 50% and 35%, respectively, compared with the control. Whereas there was no significant difference between the effect of 18 nmol/L triptolide and that of anti-MMP-9 on invasive potential of HT-1080 cells.ConclusionsThese data suggest that triptolide inhibits tumor cell invasion partly by reducing MMP-9 gene expression and activity

On Newton Screening

Screening and working set techniques are important approaches to reducing the size of an optimization problem. They have been widely used in accelerating first-order methods for solving large-scale sparse learning problems. In this paper, we develop a new screening method called Newton screening (NS) which is a generalized Newton method with a built-in screening mechanism. We derive an equivalent KKT system for the Lasso and utilize a generalized Newton method to solve the KKT equations. Based on this KKT system, a built-in working set with a relatively small size is first determined using the sum of primal and dual variables generated from the previous iteration, then the primal variable is updated by solving a least-squares problem on the working set and the dual variable updated based on a closed-form expression. Moreover, we consider a sequential version of Newton screening (SNS) with a warm-start strategy. We show that NS possesses an optimal convergence property in the sense that it achieves one-step local convergence. Under certain regularity conditions on the feature matrix, we show that SNS hits a solution with the same signs as the underlying true target and achieves a sharp estimation error bound with high probability. Simulation studies and real data analysis support our theoretical results and demonstrate that SNS is faster and more accurate than several state-of-the-art methods in our comparative studies