Toward Globally Optimal State Estimation Using Automatically Tightened Semidefinite Relaxations

In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted redundant constraints are required to obtain tight relaxations and thus global optimality. These constraints are formulation-dependent and typically require a lengthy manual process to find. Instead, the present paper suggests an automatic method to find a set of sufficient redundant constraints to obtain tightness, if they exist. We first propose an efficient feasibility check to determine if a given set of variables can lead to a tight formulation. Secondly, we show how to scale the method to problems of bigger size. At no point of the process do we have to manually find redundant constraints. We showcase the effectiveness of the approach, in simulation and on real datasets, for range-based localization and stereo-based pose estimation. Finally, we reproduce semidefinite relaxations presented in recent literature and show that our automatic method finds a smaller set of constraints sufficient for tightness than previously considered.Comment: 18 pages, 20 figure

Regulation by PGE(2) of the production of interleukin-6, macrophage colony stimulating factor, and vascular endothelial growth factor in human synovial fibroblasts

1. We examined the effects of endogenous prostaglandin E(2) (PGE(2)) on the production of interleukin-6 (IL-6), macrophage colony stimulating factor (M-CSF), and vascular endothelial growth factor (VEGF) by interleukin-1β (IL-1β)-stimulated human synovial fibroblasts. 2. NS-398 (1 μM), a cyclo-oxygenase-2 (COX-2) inhibitor, inhibited IL-6 and VEGF production (35±4% and 26±2%, respectively) but enhanced M-CSF production (38±4%) by IL-1β (1 ng ml(−1)) in synovial fibroblasts isolated from patients with osteoarthritis (OA) and rheumatoid arthritis (RA). Exogenous PGE(2) completely abolished the effects of NS-398 on the production of each mediator by OA fibroblasts stimulated with IL-1β. 3. 8-Bromo cyclic AMP and dibutyryl cyclic AMP, cyclic AMP analogues, mimicked the effects of PGE(2) on IL-6, M-CSF, and VEGF production by OA fibroblasts. 4. The EP(2) selective receptor agonist ONO-AE1-259 (2 nM) and the EP(4) selective receptor agonist ONO-AE1-329 (2 or 20 nM), but not the EP(1) selective receptor agonist ONO-DI-004 (1 μM) and the EP(3) selective receptor agonist ONO-AE-248 (1 μM), replaced the effects of PGE(2) on IL-6, M-CSF, and VEGF production by OA and RA fibroblasts stimulated with IL-1β in the presence of NS-398. 5. Both OA and RA fibroblasts expressed mRNA encoding EP(2) and EP(4) but not EP(1) receptors. In addition, up-regulation of EP(2) and EP(4) receptor mRNAs was observed at 3 h after IL-1β treatment. 6. These results suggest that endogenous PGE(2) regulates the production of IL-6, M-CSF, and VEGF by IL-1β-stimulated human synovial fibroblasts through the activation of EP(2) and EP(4) receptors with increase in cyclic AMP