21 citations · 151 across the 30 of their papers we have counts for
32 papers · 1 filter
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),…
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…
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…
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…
Tight error bounds for log-determinant cones without constraint qualifications
Ying Lin, Scott B. Lindstrom, Bruno F. Lourenço +1
In this paper, without requiring any constraint qualifications, we establish tight error bounds for the log-determinant cone, which is the closure of the hypograph of the perspecti…
Non-facial exposedness of copositive cones over symmetric cones
Mitsuhiro Nishijima, Bruno F. Lourenço
In this paper, we consider copositive cones over symmetric cones and show that they are never facially exposed when the underlying cone has dimension at least 2. We do so by explic…
Eigenvalue programming beyond matrices
Masaru Ito, Bruno F. Lourenço
In this paper we analyze and solve eigenvalue programs, which consist of the task of minimizing a function subject to constraints on the "eigenvalues" of the decision variable. Her…
Generalized power cones: optimal error bounds and automorphisms
Ying Lin, Scott B. Lindstrom, Bruno F. Lourenço +1
Error bounds are a requisite for trusting or distrusting solutions in an informed way. Until recently, provable error bounds in the absence of constraint qualifications were unatta…
Automorphisms of rank-one generated hyperbolicity cones and their derivative relaxations
Masaru Ito, Bruno F. Lourenço
A hyperbolicity cone is said to be rank-one generated (ROG) if all its extreme rays have rank one, where the rank is computed with respect to the underlying hyperbolic polynomial.…
Self-dual polyhedral cones and their slack matrices
João Gouveia, Bruno F. Lourenço
We analyze self-dual polyhedral cones and prove several properties about their slack matrices. In particular, we show that self-duality is equivalent to the existence of a positive…
A Simplified Treatment of Ramana's Exact Dual for Semidefinite Programming
Bruno F. Lourenço, Gábor Pataki
In semidefinite programming the dual may fail to attain its optimal value and there could be a duality gap, i.e., the primal and dual optimal values may differ. In a striking paper…
Optimal error bounds in the absence of constraint qualifications with applications to the -cones and beyond
Scott B. Lindstrom, Bruno F. Lourenço, Ting Kei Pong
We prove tight Hölderian error bounds for all -cones. Surprisingly, the exponents differ in several ways from those that have been previously conjectured; moreover, they illumin…
Hyperbolicity cones are amenable
Bruno F. Lourenço, Vera Roshchina, James Saunderson
Amenability is a notion of facial exposedness for convex cones that is stronger than being facially dual complete (or "nice") which is, in turn, stronger than merely being facially…
Amenable cones are particularly nice
Bruno F. Lourenço, Vera Roshchina, James Saunderson
Amenability is a geometric property of convex cones that is stronger than facial exposedness and assists in the study of error bounds for conic feasibility problems. In this paper…
Error bounds, facial residual functions and applications to the exponential cone
Scott B. Lindstrom, Bruno F. Lourenço, Ting Kei Pong
We construct a general framework for deriving error bounds for conic feasibility problems. In particular, our approach allows one to work with cones that fail to be amenable or eve…
Convergence analysis under consistent error bounds
Tianxiang Liu, Bruno F. Lourenço
We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This framework goes beyond the classical…
Random projection of Linear and Semidefinite problem with linear inequalities
Pierre-Louis Poirion, Bruno F. Lourenço, Akiko Takeda
The Johnson-Lindenstrauss Lemma states that there exist linear maps that project a set of points of a vector space into a space of much lower dimension such that the Euclidean dist…
A Limiting Analysis on Regularization of Singular SDP and its Implication to Infeasible Interior-point Algorithms
Takashi Tsuchiya, Bruno F. Lourenco, Masakazu Muramatsu +1
We consider primal-dual pairs of semidefinite programs and assume that they are ill-posed, i.e., both primal and dual are either weakly feasible or weakly infeasible. Under such ci…
Generalized subdifferentials of spectral functions over Euclidean Jordan algebras
Bruno F. Lourenço, Akiko Takeda
This paper is devoted to the study of generalized subdifferentials of spectral functions over Euclidean Jordan algebras. Spectral functions appear often in optimization problems pl…
The automorphism group and the non-self-duality of -cones
Masaru Ito, Bruno F. Lourenço
In this paper, we determine the automorphism group of the -cones () in dimension greater than two. In particular, we show that the automorphism group of those -cones…
Amenable cones: error bounds without constraint qualifications
Bruno F. Lourenço
We provide a framework for obtaining error bounds for linear conic problems without assuming constraint qualifications or regularity conditions. The key aspects of our approach are…
Exact augmented Lagrangian functions for nonlinear semidefinite programming
Ellen H. Fukuda, Bruno F. Lourenço
In this paper, we study augmented Lagrangian functions for nonlinear semidefinite programming (NSDP) problems with exactness properties. The term exact is used in the sense that th…
An extension of Chubanov's algorithm to symmetric cones
Bruno F. Lourenço, Tomonari Kitahara, Masakazu Muramatsu +1
In this work we present an extension of Chubanov's algorithm to the case of homogeneous feasibility problems over a symmetric cone K. As in Chubanov's method for linear feasibility…