We propose a convex optimization formulation with the Ky Fan 2-k-norm and l1-norm to fi nd k largest approximately rank-one submatrix blocks of a given nonnegative matrix that has low-rank block diagonal structure with noise. We analyze low-rank and sparsity structures of the optimal solutions using properties of these two matrix norms. We show that, under … Read more
In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very broad as a reliable solution to the problem would provide a powerful modeling tool in many areas of experimental science. We … Read more
Abstract—In this paper, we present a method to solve inverse problems of electromagnetic circuit design which are formulated as a topology optimization problem. Indeed, by imposing the magnetic field inside a region, we search a best material distribution into variable domains. In order to perform this, we minimize the quadratic error between the prescribed magnetic … Read more
In this paper we consider bound constrained global optimization problems where first-order derivatives of the objective function can be neither computed nor approximated explicitly. For the solution of such problems the DIRECT Algorithm has been proposed which has strong convergence properties and a good ability to locate promising regions of the feasible domain. However, the … Read more
Typical challenges of simulation-based design optimization include unavailable gradients and unreliable approximations thereof, expensive function evaluations, numerical noise, multiple local optima and the failure of the analysis to return a value to the optimizer. One possible remedy to alleviate these issues is to use surrogate models in lieu of the computational models or simulations and … Read more
We study the maximum likelihood model in emission tomography and propose a new family of algorithms for its solution, called String-Averaging Expectation-Maximization (SAEM). In the String-Averaging algorithmic regime, the index set of all underlying equations is split into subsets, called “strings,” and the algorithm separately proceeds along each string, possibly in parallel. Then, the end-points … Read more
We apply the recently proposed superiorization methodology (SM) to the inverse planning problem in radiation therapy. The inverse planning problem is represented here as a constrained minimization problem of the total variation (TV) of the intensity vector over a large system of linear two-sided inequalities. The SM can be viewed conceptually as lying between feasibility-seeking … Read more
Filter networks are used as a powerful tool aimed at reducing the image processing time and maintaining high image quality. They are composed of sparse sub-filters whose high sparsity ensures fast image processing. The filter network design is related to solving a sparse optimization problem where a cardinality constraint bounds above the sparsity level. In … Read more
Abstract The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi- Newton updating techniques for deterministic optimization leads to noisy curvature estimates that have harmful effects on the robustness of the iteration. In this paper, we propose a stochastic quasi-Newton method that is efficient, robust … Read more
We consider the task of classification in the high-dimensional setting where the number of features of the given data is significantly greater than the number of observations. To accomplish this task, we propose sparse zero-variance discriminant analysis (SZVD) as a method for simultaneouslyperforming linear discriminant analysis and feature selection on high-dimensional data. This method combines … Read more