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Exploiting structure in nonconvex quadratic optimisation

Radu Baltean-Lugojan, Ruth Misener, Panos Parpas, Engineering And Physical Sciences Research Council, IBM
Finding globally-optimal solutions in quadratic nonconvex optimisation problems deterministically at scale requires exploiting problem structure.  ...  The structure this interplay introduces is difficult to exploit due to different existing mathematical/algorithmic toolboxes for nonlinear-continuous versus discrete-polyhedral optimisation.  ...  Chapter 7 Conclusions and Future Work This thesis studies how structure can be exploited in deterministic quadratic nonconvex optimisation, both within the specific class of commercially-relevant standard  ... 
doi:10.25560/79281 fatcat:ihc7fhtr7bfffivjxe7hqgw62e

Safety-Aware Optimal Control in Motion Planning [article]

Han Wang, Xuda Ding, Jianping He, Kostas Margellos, Antonis Papachristodoulou
2022 arXiv   pre-print
Optimisation is a popular tool of generating control laws for motion planning in a complex environment.  ...  The existence of multiple irregular obstacles in the working space introduces nonconvex collision avoidance constraints, making the optimal control problem intractable.  ...  The quadratically convexified constraints enable us to solve the optimisation sub-problem in Step 2.  ... 
arXiv:2204.13380v1 fatcat:szvunmaktfcnfbsjp47bswh4dq

Improving an optimization-based framework for sensitivity analysis in multi-criteria decision-making

L.G. Proll, A. Salhi, D. Rios Insua
2001 Journal of Multi-Criteria Decision Analysis  
programmes, 1 nonconvex quadratic programme and 1 nonconvex nonlinear programme with distance analysis performed in the L 1 , L 2 , and L ∞ metrics.  ...  Its success arises from exploiting the structure of the problem constraints to ensure that random neighbours of the current point are always feasible.  ... 
doi:10.1002/mcda.283 fatcat:vn6qjf4xy5ec5ph25fax4dm3a4

Symmetry Detection for Quadratically Constrained Quadratic Programs Using Binary Layered Graphs [article]

Georgia Kouyialis, Ruth Misener
2019 arXiv   pre-print
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm.  ...  This work develops methods for detecting groups of symmetry in the formulation of quadratically constrained quadratic optimisation problems via adjacency matrices.  ...  Section 3 formally defines symmetry in quadratically constrained quadratic optimisation problems and identifies the role of integrality and nonconvexity in such cases.  ... 
arXiv:1712.05222v4 fatcat:ieopnho76bht3hmjg4pynaqhsm

Optimal Learning from Verified Training Data

Nick Bishop, Long Tran-Thanh, Enrico Gerding
2020 Neural Information Processing Systems  
Although the resulting optimisation problem is nonconvex, we derive an algorithm which converges globally, outperforming current approaches which only guarantee convergence to local optima.  ...  In attempts to relax this assumption, fields such as adversarial learning typically assume that data is provided by an adversary, whose sole objective is to fool a learning algorithm.  ...  In particular, in Section 6, we shall exploit Theorem 1 to circumvent the nonconvexities present in the fractional formulation of our SPG.  ... 
dblp:conf/nips/BishopTG20 fatcat:xittfpclovdm7ipq6kdmwuzwhu

An interior-point implementation developed and tuned for radiation therapy treatment planning

Sebastiaan Breedveld, Bas van den Berg, Ben Heijmen
2017 Computational optimization and applications  
In this paper we describe an implementation specifically designed for optimisation in radiation therapy.  ...  These problems are large-scale nonlinear (and sometimes nonconvex) constrained optimisation problems, consisting of both sparse and dense data.  ...  Compliance with ethical standards Conflict of inerest This work was in part made possible by funding from Accuray Inc, Sunnyvale, USA and Elekta AB, Stockholm, Sweden.  ... 
doi:10.1007/s10589-017-9919-4 fatcat:vgfmj2pgyjez7evwff35gdvmrq

A New Approach in Deterministic Global Optimisation of Problems with Ordinary Differential Equations [chapter]

B. Chachuat, M. A. Latifi
2004 Nonconvex Optimization and Its Applications  
Each nonconvex functional in the original problem is underestimated by adding a separate convex quadratic term.  ...  This paper presents an alternative approach to the deterministic global optimisation of problems with ordinary differential equations in the constraints.  ...  They exploit special structural properties of linear systems in a composition approach to build convex relaxation of the original nonconvex problem.  ... 
doi:10.1007/978-1-4613-0251-3_5 fatcat:vp7prp62bffbrad2zrmqvzdkta

A Review of Safe Online Learning for Nonlinear Control Systems

Matthew Osborne, Hyo-Sang Shin, Antonios Tsourdos
2021 2021 International Conference on Unmanned Aircraft Systems (ICUAS)  
It is the first paper to our knowledge that compares key attributes and advantages of each technique in one paper.  ...  Nonconvex Techniques Nonconvex techniques are needed for problems with multiple optimisation parameters problem or when the system is highly nonlinear.  ...  The possibly nonconvex optimisation is augmented with random sampling to increase convergence guarantees. Speed of optimisation is also achieved via parallel computation of algorithm equations. H.  ... 
doi:10.1109/icuas51884.2021.9476765 fatcat:6uf4ad73ynccbgtbo7sqkn3qty

Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization (Dagstuhl Seminar 18081)

Pierre Bonami, Ambros M. Gleixner, Jeff Linderoth, Ruth Misener, Michael Wagner
2018 Dagstuhl Reports  
Current obstacles include characterizing the computability boundary, effectively exploiting known optimization technologies for specialized classes of MINLP, and effectively using logical formulas holistically  ...  MINLP has transitioned to a forefront position in computer science, with researchers actively developing MINLP theory, algorithms, and implementations.  ...  It exploits structure to reduce function evaluation time including Jacobian and Hessian computation.  ... 
doi:10.4230/dagrep.8.2.64 dblp:journals/dagstuhl-reports/BonamiGLM18 fatcat:fn6llvricbevzjsm4teuf5xuha

Adaptive channel estimation for cognitive fully adaptive radar

Bosung Kang, Sandeep Gogineni, Muralidhar Rangaswamy, Joseph R. Guerci, Erik Blasch
2021 IET radar, sonar & navigation  
Using the fact that adjacent channel transfer functions have a close relationship in terms of a cosine similarity metric, the cosine similarity constraint can be exploited in the least squares problem.  ...  The paper also proposes a new optimisation problem with an additional inner product constraint, which results in a convex second-order cone programming (SOCP) and is robust to the signal-to-noise ratio  ...  In other words, the FD approach does not exploit any further structural information or relationship between adjacent channel transfer functions in the estimation problem.  ... 
doi:10.1049/rsn2.12215 fatcat:vx7z4zzidzfarimiqvgqnvfuie

A CNC approach for Directional Total Variation [article]

Gabriele Scrivanti, Emilie Chouzenoux, Jean-Christophe Pesquet
2022 arXiv   pre-print
We additionally propose an efficient optimisation strategy for the resulting convex minimisation problem.  ...  By suitably exploiting duality properties, our formulation allows to encompass sophisticated directional total variation (DTV) priors.  ...  In the next section, we investigate how to address Problem (12) by means of an optimisation scheme that exploits the structure of this objective function. IV. OPTIMISATION ALGORITHM A.  ... 
arXiv:2209.01376v1 fatcat:6bmvrnxbwrgx5hqxndt4r35c2y

Comparing MIQCP Solvers to a Specialised Algorithm for Mine Production Scheduling [chapter]

Andreas Bley, Ambros M. Gleixner, Thorsten Koch, Stefan Vigerske
2012 Modeling, Simulation and Optimization of Complex Processes  
The computational results presented show that general-purpose solvers with no particular knowledge of problem structure are able to nearly match the performance of a hand-crafted algorithm.  ...  This paper investigates the performance of several out-ofthe-box solvers for mixed-integer quadratically constrained programmes (MIQCPs) on an open pit mine production scheduling problem with mixing constraints  ...  This structure is not directly exploited by the general-purpose solvers.  ... 
doi:10.1007/978-3-642-25707-0_3 dblp:conf/hpsc/BleyGKV09 fatcat:eymdh7v7cnevjptn2vysomgztq

A Guide to Conic Optimisation and its Applications

Adam N. Letchford, Andrew J. Parkes
2018 Reserche operationelle  
In this invited paper, we give a gentle introduction to conic optimisation, followed by a survey of applications in OR and related areas.  ...  Many are however unaware of conic optimisation, which is a powerful generalisation of LP, with a prodigious array of important real-life applications.  ...  Non-convex quadratic (and polynomial) optimisation Finally, we consider general quadratic optimisation problems, and their natural generalisation, polynomial optimisation problems.  ... 
doi:10.1051/ro/2018034 fatcat:mj3kcw7oh5dqbikuqbttjscemy

Hybrid Methods in Solving Alternating-Current Optimal Power Flows

Jie Liu, Alan Claude Liddell, Jakub Marecek, Martin Takac
2017 IEEE Transactions on Smart Grid  
Many steady-state problems in power systems, including rectangular power-voltage formulations of optimal power flows in the alternating-current model (ACOPF), can be cast as polynomial optimisation problems  ...  This has motivated much research into alternative, elaborate relaxations, often exploiting treelike structures.  ...  [6] , [7] showed, however, that it can be cast as a certain nonconvex semidefinite optimisation problem.  ... 
doi:10.1109/tsg.2017.2715282 fatcat:jwgr23ohtfcr3giq7xixvfelxy

A tutorial on model predictive control for spacecraft rendezvous

Edward N. Hartley
2015 2015 European Control Conference (ECC)  
Since MPC implementation relies on finding the solution to constrained optimisation problems in real-time, computational aspects are also briefly examined.  ...  This tutorial paper provides a review of recent advances in the field of spacecraft rendezvous using model predictive control (MPC), an advanced optimal control strategy based on on-line constrained optimisation  ...  Examples include CVXGEN [53] and FORCES [54] which are online code-generators to generate custom structure-exploiting IP solvers.  ... 
doi:10.1109/ecc.2015.7330727 dblp:conf/eucc/Hartley15 fatcat:szfwzeuuyvd5tmoueierbwq3xy
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