Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data

We consider the problem of minimizing a smooth convex objective function subject to the set of minima of another differentiable convex function. In order to solve this problem, we propose an algorithm which combines the gradient method with a penalization technique. Moreover, we insert in our algorithm an inertial term, which is able to take advantage of the history of the iterates. We show weak convergence of the generated sequence of iterates to an optimal solution of the optimization problem, provided a condition expressed via the Fenchel conjugate of the constraint function is fulfilled. We also prove convergence for the objective function values to the optimal objective value. The convergence analysis carried out in this paper relies on the celebrated Opial Lemma and generalized Fejér monotonicity techniques. We illustrate the functionality of the method via a numerical experiment addressing image classification via support vector machines.     

Extrapolated sequential constraint method for variational inequality over the intersection of fixed-point sets

Numerical Algorithms - In this paper, the convergence and dynamics of improved Chebyshev-Secant-type iterative methods are studied for solving nonlinear equations in Banach space settings. Their...     

Adaptive subgradient method for the split quasi-convex feasibility problems

In this paper, we consider a type of the celebrated convex feasibility problem, named as split quasi-convex feasibility problem (SQFP). The SQFP is to find a point in a sublevel set of a quasi-convex function in one space and its image under a bounded linear operator is contained in a sublevel set of another quasi-convex function in the image space. We propose a new adaptive subgradient algorithm for solving SQFP problem. We also discuss the convergence analyses for two cases: the first case where the functions are upper semicontinuous in the setting of finite dimensional, and the second case where the functions are weakly continuous in the infinite-dimensional settings. Finally some numerical examples in order to support the convergence results are given.     

Doubly Strapped Zwitterionic NIR-I and NIR-II Heptamethine Cyanine Dyes for Bioconjugation and Fluorescence Imaging

Heptamethine cyanine dyes enable deep tissue fluorescence imaging in the near infrared (NIR) window. Small molecule conjugates of the benchmark dye ZW800-1 have been tested in humans. However, long-term imaging protocols using ZW800-1 conjugates are limited by their instability, primarily because the chemically labile C4′-O-aryl linker is susceptible to cleavage by biological nucleophiles. Here, we report a modular synthetic method that produces novel doubly strapped zwitterionic heptamethine cyanine dyes, including a structural analogue of ZW800-1 , with greatly enhanced dye stability. NIR-I and NIR-II versions of these doubly strapped dyes can be conjugated to proteins, including monoclonal antibodies, without causing undesired fluorophore degradation or dye stacking on the protein surface. The fluorescent antibody conjugates show excellent tumor-targeting specificity in a xenograft mouse tumor model. The enhanced stability provided by doubly strapped molecular design will enable new classes of in vivo NIR fluorescence imaging experiments with possible translation to humans.     

Extrapolated cyclic subgradient projection methods for the convex feasibility problems and their numerical behaviour

ABSTRACT

We present two versions of the extrapolated cyclic subgradient projections method for solving the convex feasibility problem. Moreover, we present the results of numerical tests, where we compare the methods with the classical cyclic subgradient projections method.