Sorry, you need to enable JavaScript to visit this website.

Non-convex Optimization

Improving Graph Trend Filtering with Non-Convex Penalties


In this paper, we study the denoising of piecewise smooth graph sig-nals that exhibit inhomogeneous levels of smoothness over a graph. We extend the graph trend filtering framework to a family of non-convex regularizers that exhibit superior recovery performance overexisting convex ones. We present theoretical results in the form ofasymptotic error rates for both generic and specialized graph models. We further present an ADMM-based algorithm to solve the proposedoptimization problem and analyze its convergence.

Paper Details

Authors:
Rohan Varma, Jelena Kovačević
Submitted On:
9 June 2019 - 8:24pm
Short Link:
Type:
Event:
Presenter's Name:
Paper Code:
Document Year:
Cite

Document Files

ICASSP_poster.pdf

(58)

Keywords

Additional Categories

Subscribe

[1] Rohan Varma, Jelena Kovačević, "Improving Graph Trend Filtering with Non-Convex Penalties", IEEE SigPort, 2019. [Online]. Available: http://sigport.org/4551. Accessed: Aug. 19, 2019.
@article{4551-19,
url = {http://sigport.org/4551},
author = {Rohan Varma; Jelena Kovačević },
publisher = {IEEE SigPort},
title = {Improving Graph Trend Filtering with Non-Convex Penalties},
year = {2019} }
TY - EJOUR
T1 - Improving Graph Trend Filtering with Non-Convex Penalties
AU - Rohan Varma; Jelena Kovačević
PY - 2019
PB - IEEE SigPort
UR - http://sigport.org/4551
ER -
Rohan Varma, Jelena Kovačević. (2019). Improving Graph Trend Filtering with Non-Convex Penalties. IEEE SigPort. http://sigport.org/4551
Rohan Varma, Jelena Kovačević, 2019. Improving Graph Trend Filtering with Non-Convex Penalties. Available at: http://sigport.org/4551.
Rohan Varma, Jelena Kovačević. (2019). "Improving Graph Trend Filtering with Non-Convex Penalties." Web.
1. Rohan Varma, Jelena Kovačević. Improving Graph Trend Filtering with Non-Convex Penalties [Internet]. IEEE SigPort; 2019. Available from : http://sigport.org/4551

Global Energy Efficiency Maximization in Non-Orthogonal Interference Networks


Energy efficient resource allocation in interference networks is a challenging global optimization problem. The main issue is that the computational complexity grows exponentially in the number of variables. In general, resource allocation in interference networks requires optimizing jointly over achievable rates and transmit powers. However, close scrutiny reveals that the non-convexity stems mostly from the powers while the problem is linear in the rates.

Paper Details

Authors:
Submitted On:
8 May 2019 - 2:48am
Short Link:
Type:
Event:
Presenter's Name:
Paper Code:
Document Year:
Cite

Document Files

Global Energy Efficiency Maximization in Non-Orthogonal Interference Networks

(27)

Keywords

Additional Categories

Subscribe

[1] , "Global Energy Efficiency Maximization in Non-Orthogonal Interference Networks", IEEE SigPort, 2019. [Online]. Available: http://sigport.org/4026. Accessed: Aug. 19, 2019.
@article{4026-19,
url = {http://sigport.org/4026},
author = { },
publisher = {IEEE SigPort},
title = {Global Energy Efficiency Maximization in Non-Orthogonal Interference Networks},
year = {2019} }
TY - EJOUR
T1 - Global Energy Efficiency Maximization in Non-Orthogonal Interference Networks
AU -
PY - 2019
PB - IEEE SigPort
UR - http://sigport.org/4026
ER -
. (2019). Global Energy Efficiency Maximization in Non-Orthogonal Interference Networks. IEEE SigPort. http://sigport.org/4026
, 2019. Global Energy Efficiency Maximization in Non-Orthogonal Interference Networks. Available at: http://sigport.org/4026.
. (2019). "Global Energy Efficiency Maximization in Non-Orthogonal Interference Networks." Web.
1. . Global Energy Efficiency Maximization in Non-Orthogonal Interference Networks [Internet]. IEEE SigPort; 2019. Available from : http://sigport.org/4026

Optimal Resource Allocation for Non-Regenerative Multiway Relaying with Rate Splitting


Optimal resource allocation in interference networks requires the solution of non-convex optimization problems. Except from treating interference as noise (IAN) one usually has to optimize jointly over the achievable rates and transmit powers. This non-convexity is normally only due to the transmit powers while the rates are linear. Conventional approaches like the Polyblock Algorithm treat all variables equally and, thus, require a two layer solver to exploit the linearity in the rates and keep the computational complexity at a reasonable level.

Paper Details

Authors:
Submitted On:
21 June 2018 - 11:11am
Short Link:
Type:
Event:
Presenter's Name:
Document Year:
Cite

Document Files

Poster

(106)

Keywords

Additional Categories

Subscribe

[1] , "Optimal Resource Allocation for Non-Regenerative Multiway Relaying with Rate Splitting", IEEE SigPort, 2018. [Online]. Available: http://sigport.org/3282. Accessed: Aug. 19, 2019.
@article{3282-18,
url = {http://sigport.org/3282},
author = { },
publisher = {IEEE SigPort},
title = {Optimal Resource Allocation for Non-Regenerative Multiway Relaying with Rate Splitting},
year = {2018} }
TY - EJOUR
T1 - Optimal Resource Allocation for Non-Regenerative Multiway Relaying with Rate Splitting
AU -
PY - 2018
PB - IEEE SigPort
UR - http://sigport.org/3282
ER -
. (2018). Optimal Resource Allocation for Non-Regenerative Multiway Relaying with Rate Splitting. IEEE SigPort. http://sigport.org/3282
, 2018. Optimal Resource Allocation for Non-Regenerative Multiway Relaying with Rate Splitting. Available at: http://sigport.org/3282.
. (2018). "Optimal Resource Allocation for Non-Regenerative Multiway Relaying with Rate Splitting." Web.
1. . Optimal Resource Allocation for Non-Regenerative Multiway Relaying with Rate Splitting [Internet]. IEEE SigPort; 2018. Available from : http://sigport.org/3282

The Landscape of Non-convex Quadratic Feasibility


Motivated by applications such as ordinal embedding and collaborative ranking, we formulate homogeneous quadratic feasibility as an unconstrained, non-convex minimization problem. Our work aims to understand the landscape (local minimizers and global minimizers) of the non-convex objective, which corresponds to hinge losses arising from quadratic constraints. Under certain assumptions, we give necessary conditions for non-global, local minimizers of our objective and additionally show that in two dimensions, every local minimizer is a global minimizer.

Paper Details

Authors:
Lalit Jain, Laura Balzano
Submitted On:
19 April 2018 - 2:10pm
Short Link:
Type:
Event:
Presenter's Name:
Paper Code:
Document Year:
Cite

Document Files

ICASSP_v4.pdf

(145)

Keywords

Additional Categories

Subscribe

[1] Lalit Jain, Laura Balzano, "The Landscape of Non-convex Quadratic Feasibility", IEEE SigPort, 2018. [Online]. Available: http://sigport.org/2798. Accessed: Aug. 19, 2019.
@article{2798-18,
url = {http://sigport.org/2798},
author = {Lalit Jain; Laura Balzano },
publisher = {IEEE SigPort},
title = {The Landscape of Non-convex Quadratic Feasibility},
year = {2018} }
TY - EJOUR
T1 - The Landscape of Non-convex Quadratic Feasibility
AU - Lalit Jain; Laura Balzano
PY - 2018
PB - IEEE SigPort
UR - http://sigport.org/2798
ER -
Lalit Jain, Laura Balzano. (2018). The Landscape of Non-convex Quadratic Feasibility. IEEE SigPort. http://sigport.org/2798
Lalit Jain, Laura Balzano, 2018. The Landscape of Non-convex Quadratic Feasibility. Available at: http://sigport.org/2798.
Lalit Jain, Laura Balzano. (2018). "The Landscape of Non-convex Quadratic Feasibility." Web.
1. Lalit Jain, Laura Balzano. The Landscape of Non-convex Quadratic Feasibility [Internet]. IEEE SigPort; 2018. Available from : http://sigport.org/2798

Sparse Reconstruction for Fluorescence Lifetime Imaging Microscopy with Poisson Noise


We present a novel, three-stage method to solve the fluorescence lifetime imaging problem under low-photon conditions. In particular, we reconstruct the fluorophore concentration along with its support and fluorescence lifetime from the time-dependent measurements of scattered light exiting the domain. Because detectors used for these problems are photon counting devices, measurements are corrupted by Poisson noise. Consequently, we explicitly consider Poisson noise in conjunction with SPIRAL-$\ell_p$ -- a sparsity-promoting nonconvex optimization method -- to solve this problem.

Paper Details

Authors:
Lasith Adhikari, Arnold D. Kim, Roummel F. Marcia
Submitted On:
7 December 2016 - 10:28am
Short Link:
Type:
Event:
Presenter's Name:
Document Year:
Cite

Document Files

FLIM with Poisson

(2119)

Keywords

Additional Categories

Subscribe

[1] Lasith Adhikari, Arnold D. Kim, Roummel F. Marcia, "Sparse Reconstruction for Fluorescence Lifetime Imaging Microscopy with Poisson Noise", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1406. Accessed: Aug. 19, 2019.
@article{1406-16,
url = {http://sigport.org/1406},
author = {Lasith Adhikari; Arnold D. Kim; Roummel F. Marcia },
publisher = {IEEE SigPort},
title = {Sparse Reconstruction for Fluorescence Lifetime Imaging Microscopy with Poisson Noise},
year = {2016} }
TY - EJOUR
T1 - Sparse Reconstruction for Fluorescence Lifetime Imaging Microscopy with Poisson Noise
AU - Lasith Adhikari; Arnold D. Kim; Roummel F. Marcia
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/1406
ER -
Lasith Adhikari, Arnold D. Kim, Roummel F. Marcia. (2016). Sparse Reconstruction for Fluorescence Lifetime Imaging Microscopy with Poisson Noise. IEEE SigPort. http://sigport.org/1406
Lasith Adhikari, Arnold D. Kim, Roummel F. Marcia, 2016. Sparse Reconstruction for Fluorescence Lifetime Imaging Microscopy with Poisson Noise. Available at: http://sigport.org/1406.
Lasith Adhikari, Arnold D. Kim, Roummel F. Marcia. (2016). "Sparse Reconstruction for Fluorescence Lifetime Imaging Microscopy with Poisson Noise." Web.
1. Lasith Adhikari, Arnold D. Kim, Roummel F. Marcia. Sparse Reconstruction for Fluorescence Lifetime Imaging Microscopy with Poisson Noise [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1406

Non-monotone Quadratic Potential Games with single Quadratic constraints


We consider the problem of solving a quadratic potential game with single quadratic constraints, under no monotonicity condition of the game, nor convexity in any of the player's problem. We show existence of Nash equilibria (NE) in the game, and propose a framework to calculate Pareto efficient solutions. Regarding the corresponding non-convex potential function, we show that strong duality holds with its corresponding dual problem, give existence results of solutions and present conditions for global optimality. Finally, we propose a centralized method to solve the potential problem, and a distributed version for compact constraints. We also present simulations showing convergence behavior of the proposed distributed algorithm.

Paper Details

Authors:
Santiago Zazo, Sergio Valcarcel Macua
Submitted On:
29 March 2016 - 9:57am
Short Link:
Type:
Event:
Presenter's Name:
Document Year:
Cite

Document Files

quadratic_poster.pdf

(353)

Keywords

Additional Categories

Subscribe

[1] Santiago Zazo, Sergio Valcarcel Macua, "Non-monotone Quadratic Potential Games with single Quadratic constraints", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/632. Accessed: Aug. 19, 2019.
@article{632-16,
url = {http://sigport.org/632},
author = {Santiago Zazo; Sergio Valcarcel Macua },
publisher = {IEEE SigPort},
title = {Non-monotone Quadratic Potential Games with single Quadratic constraints},
year = {2016} }
TY - EJOUR
T1 - Non-monotone Quadratic Potential Games with single Quadratic constraints
AU - Santiago Zazo; Sergio Valcarcel Macua
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/632
ER -
Santiago Zazo, Sergio Valcarcel Macua. (2016). Non-monotone Quadratic Potential Games with single Quadratic constraints. IEEE SigPort. http://sigport.org/632
Santiago Zazo, Sergio Valcarcel Macua, 2016. Non-monotone Quadratic Potential Games with single Quadratic constraints. Available at: http://sigport.org/632.
Santiago Zazo, Sergio Valcarcel Macua. (2016). "Non-monotone Quadratic Potential Games with single Quadratic constraints." Web.
1. Santiago Zazo, Sergio Valcarcel Macua. Non-monotone Quadratic Potential Games with single Quadratic constraints [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/632