We identity the optimal non-infinitesimal direction of descent for a convex function. An algorithm is developed that can theoretically minimize a subset of (non-convex) functions.
We present an optimization problem in infinite dimensions which satisfies the usual second-order sufficient condition but for which perturbed problems fail to possess solutions.
We show that the robust forward completeness for distributed parameter systems is equivalent to the existence of a corresponding Lyapunov function that increases at most exponentially along the trajectories.
We provide proof that the optimal value function of a convex parametrized optimization problem in Euclidean spaces is itself a convex function onto the extended real line.
We study the stability of a class of action functionals induced by gradients of convex functions with respect to Mosco convergence, under mild assumptions on the underlying space.
We describe a summation procedure for the construction of the optimal solution in null controllability problem for differential equation with distributed delay
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our assumptions on the differentiability of the functions are weaker than those of existing results.
We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the nonlinearities. We show that, in many common applications, the transformation model can be associated with fixed point equations involving firmly nonexpansive operators. In turn, the recovery problem is reduced to a tractable common fixed point formulation, which is solved efficiently by a provably convergent, block-iterative algorithm. Applications to signal and image recovery are demonstrated. Inconsistent problems are also addressed.
This short note provides and proves an easy algorithm to find a basic feasible solution for the Simplex Algorithm. The method uses a rule similar to Bland's rule for the initial phase of the algorithm.
Osteoclast precursors from human peripheral blood were cultured as previously described. 15 mL of heparin anti-coagulated peripheral blood was obtained by venipuncture from the patient, and a healthy age- and sex-matched control. Peripheral blood mononuclear cells (PBMCs) were isolated using Ficoll-Hypaque Solution. Cells were washed in PBS twice, and plated on 24-well plates at a density of 1×106/well at 37°C in α-MEM, supplemented with 10% FBS, 1% penicillin/streptomycin and 25 ng/ml of macrophage colony stimulating factor (M-CSF) (R&D Systems, Inc., Minneapolis, USA). 6 days later, osteoclast precursor differentiation was induced with the medium supplemented with both 25ng/ml of M-CSF and 30ng/ml RANKL (R&D Systems, Inc., Minneapolis, USA). PBMCs in three wells from each subject were cultured in the absence of M-CSF and RANKL as a negative control.7 days later, TRAP staining was performed using a kit from Sigma-Aldrich (sigma Chemical Co., St. Louis, MO, USA). TRAP-positive cells containing 3 or more nuclei were counted as OCs. 6mm*6mm bovine cortical bone slices were put into cell culture wells at the beginning of OC differentiation. 7 days after co-cultures, the slices were removed and evaluated for OC morphology and pit formation by scanning electron microscope (INCA PENTAFET X3, Oxford Instruments, Abingdon, Oxfordshire, UK).