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Jordan Algebraic Approach to Symmetric Optimization. Delft University of Technology. Delft, The Netherlands, 2007.PhD_vieira.pdf
Vieira, Manuel V. C. "The Accuracy of Interior-Point Methods Based on Kernel Functions." J. Optimization Theory and Applications. 155.2 (2012): 637-649. Abstract

For the last decade, interior-point methods that use barrier functions induced by some real univariate kernel functions have been studied. In these interior-point methods, the algorithm stops when a solution is found such that it is close (in the barrier function sense) to a point in the central path with the desired accuracy. However, this does not directly imply that the algorithm generates a solution with prescribed accuracy. Until now, this had not been appropriately addressed. In this paper, we analyze the accuracy of the solution produced by the aforementioned algorithm.

Vieira, Manuel V. C. "Interior-point methods based on kernel functions for symmetric optimization." Optimization Methods and Software. 27.3 (2012): 513-537. Abstract

We present a generalization to symmetric optimization of interior-point methods for linear optimization based on kernel functions. Symmetric optimization covers the three most common conic optimization problems: linear, second-order cone and semi-definite optimization problems. Namely, we adapt the interior-point algorithm described in Peng et al. [Self-regularity: A New Paradigm for Primal–Dual Interior-point Algorithms. Princeton University Press, Princeton, NJ, 2002.] for linear optimization to symmetric optimization. The analysis is performed through Euclidean Jordan algebraic tools and a complexity bound is derived.

Vieira, Manuel V. C. "Interior-point methods for symmetric optimization based on a class of non-coercive kernel functions." Optimization Methods and Software. 28.3 (2013): 581-599.
Anjos, Miguel F., and Manuel V. C. Vieira. "Semidefinite Resolution and Exactness of Semidefinite Relaxations for Satisfiability." Discrete Applied Mathematics. 161.18 (2013): 2812-2826.
Vieira, Manuel V. C. "Derivatives of eigenvalues and Jordan frames." Numerical Algebra, Control and Optimization. 6.2 (2016): 115-126.
Anjos, Miguel F., and Manuel V. C. Vieira. "An improved two-stage optimization-based framework for unequal-areas facility layout." Optimization Letters. 10.7 (2016): 1379-1392.
Anjos, Miguel F., and Manuel V. C. Vieira. "Mathematical Optimization Approaches for Facility Layout Problems: The State-of-the-Art and Future Research Directions." European Journal of Operational Research. 261.1 (2017): 1-16.
Anjos, Miguel F., and Manuel V. C. Vieira. "On semidefinite least squares and minimal unsatisfiability." Discrete Applied Mathematics. 217 (2017): 79-96.