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The relative pose estimation problem is important for multi-robot systems when they execute a variety of tasks cooperatively, such as cooperative sensing, multi-robot search and rescue, formation control. The finding of reliable solutions to this problem is essential, however, algorithms that guarantee to provide globally optimal solutions are still in demand. In this paper, an alternative dimensionality reduced objective function is proposed for the planar ground multi-robot relative pose estimation problem, and a new branch-and-bound (BnB) based method is developed, through which initialization is not required and the globally optimal solution is guaranteed under arbitrary noise levels. We demonstrate that the globally optimal solutions obtained via the algorithm proposed in this paper are superior than that obtained by existing classic methods such as SE-Sync algorithm when noise levels are high. Moreover, the method proposed is simple and easy to implement. [ABSTRACT FROM AUTHOR]

Although the optimal power flow (OPF) problem has been extensively studied, solving realistic OPF models that accurately represent the operating behavior of power system components remains challenging. This paper proposes a novel model for the AC OPF problem, aiming to minimize the fuel costs of thermal units while taking into account valve-point loading effects (VPLE), prohibited operation zones (POZ), multiple fuel options (MFO), and operational rules associated with the discrete tap ratios of on-load tap changer (OLTC) transformers and with the discrete shunt susceptances of capacitor/reactor banks. These rules are represented using complementarity constraints. We propose a solution approach that integrates several strategies to address the non-smooth features of the objective function related to VPLE, the disjoint constraints and functions tied to POZ and MFO, the discrete characteristics of the reactive control variables, and the complementarity constraints governing operational rules linked to voltage control devices such as OLTC transformers and capacitor/reactor banks. The resulting optimization problem is designed to be compatible with commercial solver packages. Numerical tests on the IEEE 30, 118, and 300-bus systems aim to examine the cumulative impact of these operational factors on the optimal solution. The solution strategy proposed has demonstrated its effectiveness in solving the proposed OPF problem within reasonable computation times. • This paper proposes a novel model for the AC OPF problem. • The model proposed represents operational rules governing reactive power controls. • Although used in practical, these rules have not been addressed in the literature. • The novel rules are represented using complementarity constraints. • Proposed solution approach integrates strategies to handle imposed characteristics. [ABSTRACT FROM AUTHOR]

This paper investigates a type of minimax linear fractional program (MLFP) that often occurs in practical problems such as design of electronic circuits, finance and investment. We first transform the MLFP problem into an equivalent problem (EP) by using the Charnes–Cooper transformation and introducing an auxiliary variable. A linear relaxation strategy should simplify the nonconvex parts of the constraints in (EP). For globally solving MLFP, a branch-and-bound algorithm is then developed. It integrates the presented relaxation with the one-dimensional branching. The convergence of the algorithm is demonstrated and the number of worst-case iterations is estimated. Finally, preliminary numerical experiments verify that the proposed algorithm in this article is robust and efficient for solving the tested instances. [ABSTRACT FROM AUTHOR]