8 papers
Radial-type error bounds for semidefinite feasibility problems without strict feasibility: qualitative estimates and asymptotic tightness
Mitsuhiro Nishijima, Guoyin Li, Bruno F. Lourenço
In this paper, we develop a systematic framework for deriving explicit error bounds for semidefinite feasibility problems without assuming strict feasibility (Slater's condition),…
Projection onto hyperbolicity cones and beyond: a dual Frank-Wolfe approach
Takayuki Nagano, Bruno F. Lourenço, Akiko Takeda
We discuss the problem of projecting a point onto an arbitrary hyperbolicity cone from both theoretical and numerical perspectives. While hyperbolicity cones are furnished with a g…
BoxLitE: A Faithful Knowledge Base Embedding Based on Convex Optimization
Bruno F. Lourenço, Hesham Morgan, Ana Ozaki +2
Knowledge base (KB) embeddings aim at combining the capability of classical knowledge graph embeddings to generalize the information present in facts, the ABox, with conceptual kno…
Facial structure of copositive and completely positive cones over a second-order cone
Mitsuhiro Nishijima, Bruno F. Lourenço
We classify the faces of copositive and completely positive cones over a second-order cone and investigate their dimension and exposedness properties. Then we compute two parameter…
Concrete convergence rates for common fixed point problems under Karamata regularity
Tianxiang Liu, Bruno F. Lourenço
We introduce the notion of Karamata regular operators, which is a notion of regularity that is suitable for obtaining concrete convergence rates for common fixed point problems. Th…
Error bounds for perspective cones of a class of nonnegative Legendre functions
Xiaozhou Wang, Bruno F. Lourenço, Ting Kei Pong
Error bounds play a central role in the study of conic optimization problems, including the analysis of convergence rates for numerous algorithms. Curiously, those error bounds are…