We investigate a fast optimization method for determining the minimizer of the negative Poisson likelihood function for the global analysis of fluorescence lifetime microscopy. Using the alternating optimization strategy, we iteratively solve a non-convex optimization problem to estimate the lifetime parameters and a convex optimization problem to estimate the concentration parameters. We effec...

In this paper, we study ε-generalized weak s...

Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric spaces. But unlike convex optimization, geodesically convex (g-convex) optimization is much less developed. In this paper we contribute to the understanding of g-convex optimization by developing iteration complexity analysis for several first-order algorithms on Hadamard manifolds. Specifically, we prove ...

One way to analyze Cyber-Physical Systems is by modeling them as hybrid automata. Since reachability analysis for hybrid nonlinear automata is a very challenging and computationally expensive problem, in practice, engineers try to solve the requirements falsification problem. In one method, the falsification problem is solved by minimizing a robustness metric induced by the requirements. This o...

We introduce some methods for constrained nonlinear programming that are widely used in practice and that are known under the names SQP for sequential quadratic programming and SCP for sequential convex programming. In both cases, convex subproblems are formulated, in the first case a quadratic programming problem, in the second case a separable nonlinear program in inverse variables. The metho...

Abs t rac t We introduce some methods for constrained nonlinear programming that are widely used in practice and that are known under the names SQP for sequential quadratic programming and SCP for sequential convex programming. In both cases, convex subproblems are formulated, in the first case a quadratic programming problem, in the second case a separable nonlinear program in inverse variable...

Censored quantile regression models are very useful for the analysis of censored data when standard linear models are felt to be appropriate. However, fitting censored quantile regression is hard numerically due to the fact that the objective function that has to be minimized is not convex nor concave in regressors. The performance of standard methods is not satisfactory, in particular if a hig...

We presented a separation based optimization algorithm which, rather than optimization the entire variables altogether, This would allow us to employ: 1) a class of nonlinear functions with three variables and 2) a convex quadratic multivariable polynomial, for minimization of reprojection error. Neglecting the inversion required to minimize the nonlinear functions, in this paper we demonstrate...

Knowing the fact that the main weakness of the most standard methods including k-means and hierarchical data clustering is their sensitivity to initialization and trapping to local minima, this paper proposes a modification of convex data clustering  in which there is no need to  be peculiar about how to select initial values. Due to properly converting the task of optimization to an equivalent...