18 citations · 38 across the 9 of their papers we have counts for
9 papers
Closing Duality Gaps of SDPs through Perturbation
Takashi Tsuchiya, Bruno F. Lourenço, Masakazu Muramatsu +1
Let be a primal-dual pair of SDPs with a nonzero finite duality gap. Under such circumstances, and are weakly feasible and if we perturb the…
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…
An oracle-based projection and rescaling algorithm for linear semi-infinite feasibility problems and its application to SDP and SOCP
Masakazu Muramatsu, Tomonari Kitahara, Bruno F. Lourenço +2
We point out that Chubanov's oracle-based algorithm for linear programming [5] can be applied almost as it is to linear semi-infinite programming (LSIP). In this note, we describe…
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…
Facial Reduction and Partial Polyhedrality
Bruno F. Lourenço, Masakazu Muramatsu, Takashi Tsuchiya
We present FRA-Poly, a facial reduction algorithm (FRA) for conic linear programs that is sensitive to the presence of polyhedral faces in the cone. The main goals of FRA and FRA-P…
Weak Infeasibility in Second Order Cone Programming
Bruno F. Lourenço, Masakazu Muramatsu, Takashi Tsuchiya
The objective of this work is to study weak infeasibility in second order cone programming. For this purpose, we consider a relaxation sequence of feasibility problems that mostly…
A structural geometrical analysis of weakly infeasible SDPs
Bruno F. Lourenço, Masakazu Muramatsu, Takashi Tsuchiya
In this article, we present a geometric theoretical analysis of semidefinite feasibility problems (SDFPs). This is done by decomposing a SDFP into smaller problems, in a way that p…
Solving SDP Completely with an Interior Point Oracle
Bruno F. Lourenço, Masakazu Muramatsu, Takashi Tsuchiya
We suppose the existence of an oracle which solves any semidefinite programming (SDP) problem satisfying Slater's condition simultaneously at its primal and dual sides. We note tha…
A Perturbed Sums of Squares Theorem for Polynomial Optimization and its Applications
Masakazu Muramatsu, Hayato Waki, Levent Tuncel
We consider a property of positive polynomials on a compact set with a small perturbation. When applied to a Polynomial Optimization Problem (POP), the property implies that the op…