Projection methods in conic optimization

There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called regularization algorithms for linear conic optimization, and applications in polynomial optimization. This is a presentation of the material of several recent research articles; we aim here at clarifying the ideas, presenting them in a general framework, and pointing out important techniques

Peripheral Arterial and Venous Response to Tilt Test after a 60-Day Bedrest with and without Countermeasures (ES-IBREP)

We quantified the impact of 60-day head-down bed rest (HDBR) with countermeasures on arterial and venous response to tilt. Methods: Twenty-one males: 7 control (Con), 7 resistive vibration exercise (RVE) and 7 Chinese herb (Herb) were assessed. Subjects were identified as finisher (F) or non-finishers (NF) at the post-HDBR 20-min tilt test. The cerebral (MCA), femoral (FEM) arterial flow velocity and leg vascular resistance (FRI), the portal vein section (PV), the flow redistribution ratios (MCA/FEM; MCA/PV), the tibial (Tib), gastrocnemius (Gast), and saphenous (Saph) vein sections were measured by echography and Doppler ultrasonography. Arterial and venous parameters were measured at 3-min pre-tilt in the supine position, and at 1 min before the end of the tilt. Results: At post-HDBR tilt, MCA decreased more compared with pre-HDBR tilt in the Con, RVE, and Herb groups, the MCA/FEM tended to decrease in the Con and Herb groups (not significant) but remained stable in the RVE gr. FRI dropped in the Con gr, but remained stable in the Herb gr and increased in the RVE gr. PV decreased less in the Con and Herb groups but remained unchanged in the RVE gr. MCA/PV decreased in the Con and Herb groups, but increased to a similar extent in the RVE gr. Gast section significantly increased more in the Con gr only, whereas Tib section increased more in the Con and Herb groups but not in the RVE gr. The percent change in Saph section was similar at pre- and post-HDBR tilt. Conclusion: In the Con gr, vasoconstriction was reduced in leg and splanchnic areas. RVE and Herb contributed to prevent the loss of vasoconstriction in both areas, but the effect of RVE was higher. RVE and Herb contributed to limit Gast distension whereas only RVE had a protective effect on the Tib

Estimation of Ligament Loading and Anterior Tibial Translation in Healthy and ACL-Deficient Knees During Gait and the Influence of Increasing Tibial Slope Using EMG-Driven Approach

The purpose of this study was to develop a biomechanical model to estimate anterior tibial translation (ATT), anterior shear forces, and ligament loading in the healthy and anterior cruciate ligament (ACL)-deficient knee joint during gait. This model used electromyography (EMG), joint position, and force plate data as inputs to calculate ligament loading during stance phase. First, an EMG-driven model was used to calculate forces for the major muscles crossing the knee joint. The calculated muscle forces were used as inputs to a knee model that incorporated a knee–ligament model in order to solve for ATT and ligament forces. The model took advantage of using EMGs as inputs, and could account for the abnormal muscle activation patterns of ACL-deficient gait. We validated our model by comparing the calculated results with previous in vitro, in vivo, and numerical studies of healthy and ACL-deficient knees, and this gave us confidence on the accuracy of our model calculations. Our model predicted that ATT increased throughout stance phase for the ACL-deficient knee compared with the healthy knee. The medial collateral ligament functioned as the main passive restraint to anterior shear force in the ACL-deficient knee. Although strong co-contraction of knee flexors was found to help restrain ATT in the ACL-deficient knee, it did not counteract the effect of ACL rupture. Posterior inclination angle of the tibial plateau was found to be a crucial parameter in determining knee mechanics, and increasing the tibial slope inclination in our model would increase the resulting ATT and ligament forces in both healthy and ACL-deficient knees