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A Projection Neural Network for Circular Cone Programming

Yaling Zhang, Hongwei Liu
2018 Mathematical Problems in Engineering  
A projection neural network method for circular cone programming is proposed.  ...  Since the projection on the circular cone is simple and costs less computation time, the proposed neural network requires less state variables and leads to low complexity.  ...  Problem (78) is a convex quadratic circular cone programming problem. In [14] , problem (78) is formulated as a convex quadratic second-order cone programming problem by variable transformation.  ... 
doi:10.1155/2018/4607853 fatcat:pl7tjfs6prgcxj4mvbdbcpq7bq

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  
These mixed-integer nonlinear programs (MINLP) may be used to optimize the energy use of large industrial plants, integrate renewable sources into energy networks, design biological and biomedical systems  ...  While these efforts initially proved useful, scientists, engineers, and practitioners have realized that a transformational shift in technology will be required for MINLP to achieve its full potential.  ...  Second-Order Cone Representation -When is the convex hull of a semi-algebraic set second-order cone representable?  ... 
doi:10.4230/dagrep.8.2.64 dblp:journals/dagstuhl-reports/BonamiGLM18 fatcat:fn6llvricbevzjsm4teuf5xuha

Neural Spectrahedra and Semidefinite Lifts: Global Convex Optimization of Polynomial Activation Neural Networks in Fully Polynomial-Time [article]

Burak Bartan, Mert Pilanci
2021 arXiv   pre-print
In this paper, we develop exact convex optimization formulations for two-layer neural networks with second degree polynomial activations based on semidefinite programming.  ...  More specifically, the globally optimal two-layer neural network with polynomial activations can be found by solving a semidefinite program (SDP) and decomposing the solution using a procedure we call  ...  Acknowledgements This work was partially supported by the National Science Foundation under grants IIS-1838179, ECCS-2037304, Facebook Research, Adobe Research and Stanford SystemX Alliance.  ... 
arXiv:2101.02429v1 fatcat:ljliovkqvng6he63ovfevffwgm

Page 3919 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
The authors present a neural network with single layer structure for solving nonlinear constrained optimization problems.  ...  neural network and its application to constrained optimization problems.  ... 

Book announcements

2000 Discrete Applied Mathematics  
Quotient Spaces Denseness and Separability Problems References 3. HILBERT SPACE 3.1  ...  Linear Combinations, and Linear Varieties Convexity and Cones Linear Independence and Dimension NORMED LINEAR SPACES Definition and Examples Open and Closed Sets Convergence Transformations  ...  2 Quadratic Programming Algorithms 1 The quadratic programming problem 2 4 Interior point algorithm for quadratic programming 5 Concluding remarks 6 Comments and notes References Multiple-Objective  ... 
doi:10.1016/s0166-218x(00)90007-6 fatcat:cemhaoz7rzdmdoec7pjjqiur2a

Convex Optimization with an Interpolation-based Projection and its Application to Deep Learning [article]

Riad Akrour, Asma Atamna, Jan Peters
2020 arXiv   pre-print
We then propose an optimization algorithm that follows the gradient of the composition of the objective and the projection and prove its convergence for linear objectives and arbitrary convex and Lipschitz  ...  However, both forward and backward passes of these convex layers are significantly more expensive to compute than those of a typical neural network.  ...  In the next section, we provide numerical examples for the semi-definite cone, the second order cone and the linear cone.  ... 
arXiv:2011.07016v1 fatcat:hj2q3w6a5zhrtlljaeagjgt5gu

A New Mathematical Approach based on Conic Quadratic Programming for the Stochastic Time-Cost Tradeoff Problem in Project Management

M. Reza Peyghami, Abdollah Aghaie, Hadi Mokhtari
2013 International Journal of Industrial Engineering and Production Research  
In this paper, we consider a stochastic Time-Cost Tradeoff Problem (TCTP) in PERT networks for project management, in which all activities are subjected to a linear cost function and assumed to be exponentially  ...  We then reformulate the single path TCTP as a cone quadratic program in order to apply polynomial time interior point methods to solve the reformulation.  ...  Linear programs, convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as SOCP problems, as can many other problems that do not fall into these three categories  ... 
doaj:f895682311f247f88b3f3e8cd892bab5 fatcat:7tju5s37fnfzzok34btaicrrs4

Applications of Recurrent Neural Networks to Optimization Problems [chapter]

Alaeddin Malek
2008 Recurrent Neural Networks  
While particular problems presented in this research relates to linear, quadratic and nonlinear programming, monotone variational inequalities and complementarity problems, I fell that the methodology  ...  The theoretical areas of interest include fundamental methods, models and algorithms for solving general optimization problems using artificial recurrent neural networks.  ...  Primal and dual linear programs (PLP) and (DLP) are convex programs since the set of feasible solutions to a linear program is a convex set and a linear objective function is both convex and concave.  ... 
doi:10.5772/5556 fatcat:ee7dbi2oh5fdhblhw7fnzobvhm

A Memristor-Based Optimization Framework for AI Applications [article]

Sijia Liu, Yanzhi Wang, Makan Fardad, Pramod K. Varshney
2017 arXiv   pre-print
The capability of this framework is shown by applying it to linear programming, quadratic programming, and sparse optimization.  ...  In this article, we discuss how networks of memristors arranged in crossbar arrays can be used for efficiently solving optimization and machine learning problems.  ...  There exist many variants of QP, such as a second-order cone program (SOCP) and a quadratically constrained quadratic program (QCQP) [37] .  ... 
arXiv:1710.08882v1 fatcat:dq3zoujvw5hvla2l522v7ciym4

Unfolding Projection-free SDP Relaxation of Binary Graph Classifier via GDPA Linearization [article]

Cheng Yang and Gene Cheung and Wai-tian Tan and Guangtao Zhai
2021 arXiv   pre-print
In this paper, leveraging a recent linear algebraic theorem called Gershgorin disc perfect alignment (GDPA), we unroll a projection-free algorithm for semi-definite programming relaxation (SDR) of a binary  ...  As a result, each iteration only requires computing a linear program (LP) and one extreme eigenvector.  ...  We focus on unfolding of iterative algorithms involving PSD cone projection (O'Donoghue et al. 2016 ) that are common when addressing SDR of NP-hard quadratically constrained quadratic programming (QCQP  ... 
arXiv:2109.04697v1 fatcat:fbsaqlatcndslh2ephxphvbp3u

Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete-Type Classes of SOC Complementarity Functions

Juhe Sun, Xiao-Ren Wu, B. Saheya, Jein-Shan Chen, Chun-Hsu Ko
2019 Mathematical Problems in Engineering  
This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network  ...  More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order cone is proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions  ...  inequality (SOCCVI) problem; Miao, Chen, and Ko [33] proposed a neural network model for efficiently solving general nonlinear convex programs with second-order cone constraints.  ... 
doi:10.1155/2019/4545064 fatcat:n5i6m2hq2zbx7a7ubqsoulzmfi

Enforcing robust control guarantees within neural network policies [article]

Priya L. Donti, Melrose Roderick, Mahyar Fazlyab, J. Zico Kolter
2021 arXiv   pre-print
Specifically, our approach entails integrating custom convex-optimization-based projection layers into a neural network-based policy.  ...  When designing controllers for safety-critical systems, practitioners often face a challenging tradeoff between robustness and performance.  ...  agreement between the National Science Foundation and Carnegie Mellon University (SES-00949710), the Computational Sustainability Network, and the Bosch Center for AI.  ... 
arXiv:2011.08105v2 fatcat:4dx5hd7fnba3bkvzvje7upizbe

Design of General Projection Neural Networks for Solving Monotone Linear Variational Inequalities and Linear and Quadratic Optimization Problems

Xiaolin Hu, Jun Wang
2007 IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)  
In addition, it is discovered that the designed neural network in a specific case turns out to be the primal-dual network for solving quadratic or linear programming problems.  ...  Because quadratic and linear programming problems are special cases of LVI in terms of solutions, the designed neural networks can solve them efficiently as well.  ...  In order to reduce the number of states of neural networks for quadratic programming, a simplified dual neural network was recently devised [22] .  ... 
doi:10.1109/tsmcb.2007.903706 pmid:17926722 fatcat:upwhsyaoknbeph5c2ajnisgdvy

Learning Lyapunov Functions for Piecewise Affine Systems with Neural Network Controllers [article]

Shaoru Chen, Mahyar Fazlyab, Manfred Morari, George J. Pappas, Victor M. Preciado
2020 arXiv   pre-print
function candidate as the solution to a convex program.  ...  We propose a learning-based method for Lyapunov stability analysis of piecewise affine dynamical systems in feedback with piecewise affine neural network controllers.  ...  We observe that the projected control input u p is the optimal solution to the convex quadratic program (31) .  ... 
arXiv:2008.06546v2 fatcat:exyzy35ovrag5ff63y2a4tz6gq

A Unified View of SDP-based Neural Network Verification through Completely Positive Programming [article]

Robin Brown, Edward Schmerling, Navid Azizan, Marco Pavone
2022 arXiv   pre-print
In this work, we develop an exact, convex formulation of verification as a completely positive program (CPP), and provide analysis showing that our formulation is minimal -- the removal of any constraint  ...  Verifying that input-output relationships of a neural network conform to prescribed operational specifications is a key enabler towards deploying these networks in safety-critical applications.  ...  authors and not any NSF or NASA entity.  ... 
arXiv:2203.03034v1 fatcat:2jnhieylw5dlrnw5y74ufqhhje
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