5 citations · 9 across the 5 of their papers we have counts for
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Polyhedral Analysis of Quadratic Optimization Problems with Stieltjes Matrices and Indicators
Peijing Liu, Alper Atamtürk, Andrés Gómez +1
In this paper, we consider convex quadratic optimization problems with indicators on the continuous variables. In particular, we assume that the Hessian of the quadratic term is a…
On the Softplus Penalty for Constrained Convex Optimization
Meng Li, Paul Grigas, Alper Atamturk
We study a new penalty reformulation of constrained convex optimization based on the softplus penalty function. We develop novel and tight upper bounds on the objective value gap a…
Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part II: Theoretical & Computational Results
Ramtin Madani, Mersedeh Ashraphijuo, Mohsen Kheirandishfard +1
In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxa…
Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part I: Definitions & Basic Properties
Ramtin Madani, Mersedeh Ashraphijuo, Mohsen Kheirandishfard +1
For general quadratically-constrained quadratic programming (QCQP), we propose a parabolic relaxation described with convex quadratic constraints. An interesting property of the pa…
The equivalence of optimal perspective formulation and Shor's SDP for quadratic programs with indicator variables
Shaoning Han, Andrés Gómez, Alper Atamtürk
In this paper, we compare the strength of the optimal perspective reformulation and Shor's SDP relaxation. We prove these two formulations are equivalent for quadratic optimization…
2x2 convexifications for convex quadratic optimization with indicator variables
Shaoning Han, Andrés Gómez, Alper Atamtürk
In this paper, we study the convex quadratic optimization problem with indicator variables. For the bivariate case, we describe the convex hull of the epigraph in the original spac…