We consider a class of $\ell_0$-minimization problems, which is to search for the partial sparsest solution to an underdetermined linear system with additional constraints. We introduce several concepts, including $l_p$-induced quasi-norm ($0
Many practical problems can be formulated as $\ell_0$-minimization problems with nonnegativity constraints, which seek the sparsest nonnegative solutions to underdetermined linear systems. Recent study indicates that $\ell_1$-minimization is efficient for solving some classes of $\ell_0$-minimization problems. From a mathematical point of view, however, the understanding of the relationship between $\ell_0$- and $\ell_1$-minimization remains incomplete. In … Read more
In this paper we address the problem of identifying the most likely infection pattern responsible for the spread of a disease in a network. In particular, we focus on the scenario where limited information (i.e. infection reports) is available during an ongoing outbreak. For this problem we propose a maximum likelihood model and present an … Read more
Power System planning encompasses the concept of minimization of transmission losses keeping in mind the voltage stability and system reliability. Voltage profile decides the state of a system and its control is dependent on Generator source voltage, shunt/series injection, transformer taps etc. Optimal parameter setting in system level is needed for managing the available resources … Read more
This paper investigates the population dynamics of a system of identically prepared B cells whose proliferation trajectories have been individually tracked using live-cell imaging techniques. The main goal is to investigate whether the system behavior can be determined using an optimality criterion. In order to achieve this goal we assume the existence of an intracellular … Read more
In this paper the turnpike property is established for convex optimal control problems, involving undiscounted utility function and differential inclusions defined by multi-valued mapping having convex graph. Utility function is concave but not necessarily strictly concave. The turnpike theorem is proved under the main assumption that over any given line segment, either multi-valued mapping is … Read more
We present a novel heuristic algorithm to identify feasible solutions of a mixed-integer nonlinear programming problem arising in natural gas transportation: the selection of new pipelines to enhance the network’s capacity to a desired level in a cost-efficient way. We solve this problem in a linear programming based branch-and-cut approach, where we deal with the … Read more
Finding a global solution to the optimal power flow (OPF) problem is difficult due to its nonconvexity. A convex relaxation in the form of semidefinite programming (SDP) has attracted much attention lately as it yields a global solution in several practical cases. However, it does not in all cases, and such cases have been documented … Read more
A new computational algorithm is introduced in the present study to solve multimaterial topology optimization problems. It is based on the penalization of the objective functional by the multiphase volume constrained Cahn-Hilliard energy functional. The update procedure is based on the gradient flow of the objective functional by a fractional step projected steepest descent method. … Read more
Quadratic programming problems (QPs) that arise from dynamic optimization problems typically exhibit a very particular structure. We address the ubiquitous case where these QPs are strictly convex and propose a dual Newton strategy that exploits the block-bandedness similarly to an interior-point method. Still, the proposed method features warmstarting capabilities of active-set methods. We give details … Read more