On the complexity of approximating the maximal inscribed ellipsoid for a polytope
Mathematical Programming: Series A and B
Control of uncertain systems: a linear programming approach
Control of uncertain systems: a linear programming approach
Optimization of inductor circuits via geometric programming
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Improved Complexity for Maximum Volume Inscribed Ellipsoids
SIAM Journal on Optimization
Convex Optimization
FAST TCP: motivation, architecture, algorithms, performance
IEEE/ACM Transactions on Networking (TON)
Digital Circuit Optimization via Geometric Programming
Operations Research
On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
Discrete Applied Mathematics
Optimization Methods & Software
Type Synthesis of Parallel Mechanisms
Type Synthesis of Parallel Mechanisms
Workspace analysis of 5-PRUR parallel mechanisms (3T2R)
Robotics and Computer-Integrated Manufacturing
Optimization of Actuator Forces in Cable-Based Parallel Manipulators Using Convex Analysis
IEEE Transactions on Robotics
A semidefinite programming approach to optimal unambiguous discrimination of quantum states
IEEE Transactions on Information Theory
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This paper investigates the maximal singularity-free ellipse of 3-RPR planar parallel mechanisms. The paper aims at finding the optimum ellipse, by taking into account the stroke of actuators, in which the mechanism exhibits no singularity, which is a definite asset in practice. Convex optimization is adopted for the mathematical framework of this paper which requires a matrix representation for the kinematic properties of the mechanism under study in order to solve the latter optimization problem. Based on the nature of the expressions involved in the problem, two situations may arise: dealing with either convex or non-convex expressions. Both situations are treated separately with two very fast and systematic algorithms. For the first situation, an exact method is applied while for the second one, which is a general form of the first situation, convex optimization is accompanied with an iterative procedure. The computational time for the two proposed algorithms are considerably low compared with other methods proposed in the literature which opens an avenue to use the proposed algorithms for real-time purposes.