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Real-Time Solution to Quadratically Constrained Quadratic Programs for Predictive Converter Control
2020
IFAC-PapersOnLine
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Previous work has shown that the nonlinear and nonconvex MPC problem can be equivalently formulated as a convex quadratically constrained quadratic program (QCQP). ...
Previous work has shown that the nonlinear and nonconvex MPC problem can be equivalently formulated as a convex quadratically constrained quadratic program (QCQP). ...
A recent theoretical result has shown that for certain power converter topologies, the non-convex MPC problem can be equivalently reformulated as a convex quadratically constrained quadratic program (QCQP ...
doi:10.1016/j.ifacol.2020.12.252
fatcat:njcq66bdonfdlhf3w267ynkloq
Introducing the quadratically-constrained quadratic programming framework in HPIPM
[article]
2021
arXiv
pre-print
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The aim of the new framework is unchanged, namely providing the building blocks to efficiently and reliably solve (more general classes of) optimal control problems (OCP). ...
Leveraging the modular structure of HPIPM, the new QCQP framework builds on the QP building blocks and similarly provides fast and reliable IPM solvers. ...
for non-linear OCP and MPC problems [21] . ...
arXiv:2112.11872v1
fatcat:ozg637ry7ba2vhxaab4killgve
Algorithm-Hardware Co-Optimization of the Memristor-Based Framework for Solving SOCP and Homogeneous QCQP Problems
[article]
2018
arXiv
pre-print
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This paper, as the first attempt towards this direction, proposes a novel memristor crossbar-based framework for solving two important convex optimization problems, i.e., second-order cone programming ...
Hence the memristor crossbar technology can potentially be utilized for developing low-complexity and high-scalability solution frameworks for solving a large class of convex optimization problems, which ...
To the best of our knowledge, this paper presents the first framework for solving SOCP and homogeneous QCQP problems using memristor crossbar techniques. ...
arXiv:1802.00824v1
fatcat:m7czvdbakzaprb4fts2bnnbpui
Least squares phase retrieval using feasible point pursuit
2016
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
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A least-squares (LS) formulation is adopted, and a recently developed non-convex QCQP approximation technique called feasible point pursuit (FPP) is tailored to obtain a new LS-FPP phase retrieval algorithm ...
It is revisited here through a new approach based on nonconvex quadratically constrained quadratic programming (QCQP). ...
, so P 0 belongs to a class of non-convex QCQP problems, which is NP-hard in its general form. ...
doi:10.1109/icassp.2016.7472486
dblp:conf/icassp/QianSHHS16
fatcat:nkeeop7wzbe3rcsqqo35wjvkb4
Multiple kernel learning, conic duality, and the SMO algorithm
2004
Twenty-first international conference on Machine learning - ICML '04
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We propose a novel dual formulation of the QCQP as a second-order cone programming problem, and show how to exploit the technique of Moreau-Yosida regularization to yield a formulation to which SMO techniques ...
Unfortunately, current convex optimization toolboxes can solve this problem only for a small number of kernels and a small number of data points; moreover, the sequential minimal optimization (SMO) techniques ...
Acknowledgements We wish to acknowledge support from a grant from Intel Corporation, and a graduate fellowship to Francis Bach from Microsoft Research. ...
doi:10.1145/1015330.1015424
dblp:conf/icml/BachLJ04
fatcat:vdn7dckdxfd4lhvm3nzws4zjpe
Branch-and-Bound Performance Estimation Programming: A Unified Methodology for Constructing Optimal Optimization Methods
[article]
2023
arXiv
pre-print
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We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. ...
optimality using a customized branch-and-bound algorithm. ...
First, BnB-PEP poses the problem of finding the optimal fixed-step first-order method for convex or nonconvex, smooth or nonsmooth optimization as a nonconvex but practically tractable QCQP called BnB-PEP-QCQP ...
arXiv:2203.07305v4
fatcat:tmscbnk37fh2hdsclhtimonude
Multi-class Discriminant Kernel Learning via Convex Programming
2008
Journal of machine learning research
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Based on the equivalence relationship between RKDA and least square problems in the binary-class case, we propose a convex quadratically constrained quadratic programming (QCQP) formulation for kernel ...
We show that the kernel learning problem in RKDA can be formulated as convex programs. First, we show that this problem can be formulated as a semidefinite program (SDP). ...
The implementation of the proposed QCQP formulations is based on code for SVM kernel learning provided by Dr. Gert Lanckriet. ...
dblp:journals/jmlr/YeJC08
fatcat:atidowazcbedjdvdnmozikydpe
Semidefinite Relaxation Based Blind Equalization using Constant Modulus Criterion
[article]
2018
arXiv
pre-print
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In this letter, we propose a novel scheme based on CM criterion and take advantage of the asymmetric property in a class of LDPC codes to resolve the phase ambiguity. ...
Blind equalization is a classic yet open problem. Statistic-based algorithms, such as constant modulus (CM), were widely investigated. ...
SUMMARY In this letter, we first reformulate the non-convex CM cost function into a convex SDP with rank-1 relaxation. ...
arXiv:1808.07232v2
fatcat:lrs2o7ec3zc6nkxu3fhfosjpnm
FIR Filter Design by Convex Optimization Using Directed Iterative Rank Refinement Algorithm
2016
IEEE Transactions on Signal Processing
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To obtain a rank-1 solution, we propose a novel Directed Iterative Rank Refinement (DIRR) algorithm, where at each iteration a matrix is obtained by solving a convex optimization problem. ...
By using lifting techniques, the design of a length-FIR filter can be formulated as a convex semidefinite program (SDP) in terms of an matrix that must be rank-1. ...
In [18] , a more general, non-convex filter design problem is cast as a convex problem and solved using a Goldfarb-Idnani based algorithm. ...
doi:10.1109/tsp.2016.2515062
fatcat:j2ehjvzgxzh4bo5o6yquhpapym
Constrained Multi-Slot Optimization for Ranking Recommendations
[article]
2017
arXiv
pre-print
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The problem formulation results in a quadratically constrained quadratic program (QCQP). We provide an algorithm that gives us an efficient solution by relaxing the constraints of the QCQP minimally. ...
Through simulated experiments, we show the benefits of modeling interactions in a multi-slot ranking context, and the speed and accuracy of our QCQP approximate solver against other state of the art methods ...
Art Owen for the useful discussions and his help in providing some (t, m, s)-nets for our experiments. ...
arXiv:1602.04391v2
fatcat:ewm7mcbq3bbrfa3tawsxhjf56m
Safe Zeroth-Order Convex Optimization Using Quadratic Local Approximations
[article]
2022
arXiv
pre-print
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By leveraging the knowledge of the smoothness properties of the objective and constraint functions, we propose a novel zeroth-order method, SZO-QQ, that iteratively computes quadratic approximations of ...
Through experiments, we show that our method can achieve faster convergence compared with state-of-the-art zeroth-order approaches to convex optimization. ...
Although this method can address non-convex problems and comes with a worst-case complexity that is polynomial in problem dimension, it might converge slowly, even for convex problems. ...
arXiv:2211.02645v2
fatcat:joruzt522fgrlirwtyquj2stom
Quadratic Programming with Sparsity Constraints via Polynomial Roots
[article]
2022
arXiv
pre-print
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Our main contributions are formulations of these approximations and computational methods for finding good solutions to a sparse QCQP. ...
We introduce a family of tractable approximations of such sparse QCQPs using the roots of polynomials which can be expressed as linear combinations of principal minors of a matrix. ...
also enable us to use non-positive semidefinite values for A 1 . ...
arXiv:2208.11143v2
fatcat:slmaawgvqrdrvcptsjjsyynh24
Quadratic programming-based inverse dynamics control for legged robots with sticking and slipping frictional contacts
2014
2014 IEEE/RSJ International Conference on Intelligent Robots and Systems
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We describe our method for inverse dynamics control of legged robots that can deal with both sticking and slipping frictional contacts and mitigates the problems introduced by indeterminate rigid body ...
We improve this work, which previously used quadratically constrained quadratic programs (QCQPs), to use faster-to-solve quadratic programs via linear algebraic simplifications and a nullspace. ...
However, that work used a quadratic inequality constraint, yielding a QCQP that may be insufficiently fast for high frequency control loops. ...
doi:10.1109/iros.2014.6943016
dblp:conf/iros/ZapolskyD14
fatcat:y3ywq4kf6zdcphkc2bntkgr47e
An iterative approach to nonconvex QCQP with applications in signal processing
2016
2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)
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First, this constrained problem is transformed to an unconstrained problem using a specialized penalty-based method. A tight upperbound for the alternative unconstrained objective is introduced. ...
The important design problem of multigroup multicast beamforming is formulated as a nonconvex QCQP and solved using the proposed method. ...
This means that g(q) is a convex function and we can use numerical methods like gradient descent algorithm to find the global optimum q ⋆ . ...
doi:10.1109/sam.2016.7569622
dblp:conf/ieeesam/GharanjikSSO16
fatcat:ah4kktboe5cuxk5scxketlddia
Enforcing non-positive weights for stable support vector tracking
2008
2008 IEEE Conference on Computer Vision and Pattern Recognition
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This approach ensures that the pseudo-Hessian realized within the weighted LK algorithm is positive semidefinite which allows for fast convergence and accurate alignment/tracking. ...
A further benefit of our proposed method is that the NSKM solution results in a much sparser kernel machine than the canonical SVM leading to sizeable computational savings and much improved alignment ...
fast convergence without the requirement for specifying a step-size, and (iii) is adaptive to the current iterative warp estimate. ...
doi:10.1109/cvpr.2008.4587564
dblp:conf/cvpr/Lucey08
fatcat:mcgqytvg4balvmxzv663ninqzi
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