49 citations · 107 across the 19 of their papers we have counts for
24 papers
Fair and Accurate Regression: Strong Formulations and Algorithms
Anna Deza, Andrés Gómez, Alper Atamtürk
This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regressio…
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…
State-driven Implicit Modeling for Sparsity and Robustness in Neural Networks
Alicia Y. Tsai, Juliette Decugis, Laurent El Ghaoui +1
Implicit models are a general class of learning models that forgo the hierarchical layer structure typical in neural networks and instead define the internal states based on an ``e…
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…
On the convex hull of convex quadratic optimization problems with indicators
Linchuan Wei, Alper Atamtürk, Andrés Gómez +1
We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated…
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…
Enhanced Modeling of Contingency Response in Security-constrained Optimal Power Flow
Tuncay Altun, Ramtin Madani, Alper Atamturk +2
This paper provides an enhanced modeling of the contingency response that collectively reflects high-fidelity physical and operational characteristics of power grids. Integrating a…
Supermodularity and valid inequalities for quadratic optimization with indicators
Alper Atamturk, Andres Gomez
We study the minimization of a rank-one quadratic with indicators and show that the underlying set function obtained by projecting out the continuous variables is supermodular. Alt…
Penalized Semidefinite Programming for Quadratically-Constrained Quadratic Optimization
Ramtin Madani, Mohsen Kheirandishfard, Javad Lavaei +1
In this paper, we give a new penalized semidefinite programming approach for non-convex quadratically-constrained quadratic programs (QCQPs). We incorporate penalty terms into the…
Submodular Function Minimization and Polarity
Alper Atamturk, Vishnu Narayanan
Using polarity, we give an outer polyhedral approximation for the epigraph of set functions. For a submodular function, we prove that the corresponding polar relaxation is exact; h…
Rank-one Convexification for Sparse Regression
Alper Atamturk, Andres Gomez
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with…
Sparse and Smooth Signal Estimation: Convexification of L0 Formulations
Alper Atamturk, Andres Gomez, Shaoning Han
Signal estimation problems with smoothness and sparsity priors can be naturally modeled as quadratic optimization with -"norm" constraints. Since such problems are non-conv…
A Bound Strengthening Method for Optimal Transmission Switching in Power Systems
Salar Fattahi, Javad Lavaei, Alper Atamturk
This paper studies the optimal transmission switching (OTS) problem for power systems, where certain lines are fixed (uncontrollable) and the remaining ones are controllable via on…
Successive Quadratic Upper-Bounding for Discrete Mean-Risk Minimization and Network Interdiction
Alper Atamturk, Carlos Deck, Hyemin Jeon
The advances in conic optimization have led to its increased utilization for modeling data uncertainty. In particular, conic mean-risk optimization gained prominence in probabilist…
Multi-Commodity Multi-Facility Network Design
Alper Atamturk, Oktay Gunluk
We consider multi-commodity network design models, where capacity can be added to the arcs of the network using multiples of facilities that may have different capacities. This cla…
Simplex QP-based methods for minimizing a conic quadratic objective over polyhedra
Alper Atamturk, Andres Gomez
We consider minimizing a conic quadratic objective over a polyhedron. Such problems arise in parametric value-at-risk minimization, portfolio optimization, and robust optimization…
A Spatial Branch-and-Cut Method for Nonconvex QCQP with Bounded Complex Variables
Chen Chen, Alper Atamturk, Shmuel S. Oren
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added…
Path Cover and Path Pack Inequalities for the Capacitated Fixed-Charge Network Flow Problem
Alper Atamturk, Birce Tezel, Simge Kucukyavuz
Capacitated fixed-charge network flows are used to model a variety of problems in telecommunication, facility location, production planning and supply chain management. In this pap…
A Conic Integer Programming Approach to Constrained Assortment Optimization under the Mixed Multinomial Logit Model
Alper Sen, Alper Atamturk, Philip Kaminsky
We consider the constrained assortment optimization problem under the mixed multinomial logit model. Even moderately sized instances of this problem are challenging to solve direct…
Submodularity in conic quadratic mixed 0-1 optimization
Alper Atamturk, Andres Gomez
We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. These inequalities can be utilized for solving numerous practical nonlinear discrete optimi…
Network Design with Probabilistic Capacities
Alper Atamturk, Avinash Bhardwaj
We consider a network design problem with random arc capacities and give a formulation with a probabilistic capacity constraint on each cut of the network. To handle the exponentia…
Lifted Polymatroid Inequalities for Mean-Risk Optimization with Indicator Variables
Alper Atamturk, Hyemin Jeon
We investigate a mixed 0-1 conic quadratic optimization problem with indicator variables arising in mean-risk optimization. The indicator variables are often used to model non-conv…
IPIP: A New Approach to Inverse Planning for HDR Brachytherapy by Directly Optimizing Dosimetric Indices
Timmy Siauw, Adam Cunha, Alper Atamturk +3
Purpose: Many planning methods for high dose rate (HDR) brachytherapy treatment planning require an iterative approach. A set of computational parameters are hypothesized that will…