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Economic inexact restoration for derivative-free expensive function minimization and applications

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arXiv 2020年

作者： Birgin, Ernesto G. Krejić, Natasa Martínez, José Mario Department of Computer Science Institute of Mathematics and Statistics University of São Paulo Rua do Matão 1010 Cidade Universitária SP São Paulo05508-090 Brazil Department of Mathematics and Informatics Faculty of Sciences University of Novi Sad Trg Dositeja Obradovića 4 Novi Sad21000 Serbia University of Campinas SP Campinas13083-859 Brazil

The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision. This framework allows one to obtain suitable convergence and complexity results for an approach that rationally combines low- and high-precision evaluations. In this paper we consider the case where the domain of the optimization problem is an abstract metric space. Assumptions about differentiability or even continuity will not be used in the general algorithm based on Inexact Restoration. Although optimization phases that rely on smoothness cannot be used in this case, basic convergence and complexity results are recovered. A new derivative-free optimization phase is defined and the subproblems that arise at this phase are solved using a regularization approach that takes advantage of different notions of stationarity. The new methodology is applied to the problem of reproducing a controlled experiment that mimics the failure of a *** Codes 65K05, 65K10, 90C30, 90C56, 65Y20, 90C90 Copyright © 2020, The Authors. All rights reserved.

关键词： nonlinear programming

Correlations constrained by composite measurements

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arXiv 2020年

作者： Selby, John H. Sainz, Ana Belén Magron, Victor Czekaj, Lukasz Horodecki, Michal International Centre for Theory of Quantum Technologies University of Gdańsk Gdańsk80-308 Poland LAAS-CNRS Institute of Mathematics University of Toulouse LAAS 7 Avenue du Colonel Roche Toulouse31077 Cédex 4 France

How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the correlations that physical theories may feature when restricted by some particular constraints on their measurements. We show that demanding that a theory exhibits a composite measurement imposes a hierarchy of constraints on the structure of its sets of states and effects, which translate to a hierarchy of constraints on the allowed correlations themselves. We moreover focus on the particular case where one demands the existence of a correlated measurement that reads out the parity of local fiducial measurements. By formulating a non-linear Optimisation Problem, and semidefinite relaxations of it, we explore the consequences of the existence of such a parity reading measurement for violations of Bell inequalities. In particular, we show that in certain situations this assumption has surprisingly strong consequences, namely, that Tsirelson's bound can be recovered. © 2020, CC BY.

关键词： nonlinear programming

Parallelization of the Rosen-Suzuki fist function and Himmelblau function using a two-population evolutionary algorithm

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Parallelization of the Rosen-Suzuki fist function and Himmel...

2015 International Conference on Artificial Intelligence, ICAI 2015 - WORLDCOMP 2015

作者： Scherger, Michael Molupoju, Roja Ramani Department of Computer Science Texas Christian University Fort WorthTX76129 United States Department of Computing Science Texas A and M University - Corpus Christi Corpus ChristiTX78412 United States

ISBN: (纸本)1601324073

(ICAI'15) The general nonlinear programming (NLP) problem requires finding the optimum point (minimum or maximum) of a function of n real variables subjected to some given constraints. This research presents the parallel implementation of the Rosen-Suzuki Frst function and the Himmelblau function using a two-population genetic algorithm. There are numerous situations in science and engineering where the optimum is bounded which adds complexity to the optimization problem. The approach used in this research by [32] uses evolves two populations (male and female). One population is evolved inside the feasible domain of the design space and the second population is evolved outside this feasible domain. In this research a version of this parallel, two-population algorithm was implemented. The results of this research show that the two-population parallel genetic algorithm is effective and accurate for these functions. © 2019 ICAI 2015 - WORLDCOMP 2015. All rights reserved.

关键词： nonlinear programming

Biquadratic phase-compensating system with robust stability

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Biquadratic phase-compensating system with robust stability

2019 International MultiConference of Engineers and Computer Scientists, IMECS 2019

作者： Deng, Tian-Bo Department of Information Science Faculty of Science Toho University Miyama 2-2-1 Funabashi Chiba274-8510 Japan

A new method is proposed in this paper for the design of an allpass biquadratic (biquad) phase-compensating system whose stability-margin satisfies an arbitrarily preset stability criterion. The design technique utilizes the generalized stability-triangle (GST) proposed by the author and the bilinear (BL) phase-error function of the allpass biquad system. Based on the GST condition, it is shown that the original biquad-system coefficients can be converted to the functions of other two new variables, while the two variables have no limits (bounds) on their values to satisfy the GST condition. Based on the above function conversions, the design technique further employs a nonlinear optimization method to find the optimum values of the two variables to approximate a prescribed ideal phase, while the resulting values of the two variables never violate the GST condition. That is, the resulting allpas biquad system can always satisfy a prescribed stability margin and the given ideal phase can also be best approximated in the minimax sense. An example is included in the paper to demonstrate the guaranteed stability margin. © 2019 Turkiye Klinikleri Journal of Medical Sciences. All rights reserved.

关键词： nonlinear programming

Optimizing dynamic trajectories for robustness to disturbances using polytopic projections

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arXiv 2020年

作者： Ferrolho, Henrique Merkt, Wolfgang Ivan, Vladimir Wolfslag, Wouter Vijayakumar, Sethu Institute for Perception Action and Behaviour School of Informatics University of Edinburgh 10 Crichton St EdinburghEH8 9AB United Kingdom Oxford Robotics Institute University of Oxford 23 Banbury Rd OxfordOX2 6NN United Kingdom

This paper focuses on robustness to disturbance forces and uncertain payloads. We present a novel formulation to optimize the robustness of dynamic trajectories. A straightforward transcription of this formulation into a nonlinear programming problem is not tractable for state-of-the-art solvers, but it is possible to overcome this complication by exploiting the structure induced by the kinematics of the robot. The non-trivial transcription proposed allows trajectory optimization frameworks to converge to highly robust dynamic solutions. We demonstrate the results of our approach using a quadruped robot equipped with a manipulator. Copyright © 2020, The Authors. All rights reserved.

关键词： nonlinear programming

A comparative analysis of methods related to automatic ship berthing 5

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A comparative analysis of methods related to automatic ship ...

5th International Conference on Optimization and Applications, ICOA 2019

作者： Kamil, Abdelali Allal, Abdelmoula Ait Melhaoui, Yousra Mansouri, Khalifa Rachik, Mostafa Laboratory LAMS Faculty of Sciences Ben m'Sik Hassan II University Casablanca Morocco Laboratory SSDIA ENSET Mohammedia Hassan II University Casablanca Morocco

ISBN: (纸本)9781728114828

Automatic berthing has been known as one of the most difficult problems in ship control. During port approach and berthing maneuvers, the ship master takes into account many factors before any maneuver action, i.e. ship speed, wind speed, wind direction, water current direction, available power, heading angle and ship response. However, many methods related to automatic berthing were developed by recent researches, such as Artificial Neural Network, Adaptive Backstepping, nonlinear programming and Proportional-Integral-Derivative. In this paper a comparative analysis of these methods is presented, determining the advantages and the limitations of each method. © 2019 IEEE.

关键词： nonlinear programming

A Location-based Heuristic Algorithm for Task Re-scheduling of Autonomous Agile Satellite 8

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A Location-based Heuristic Algorithm for Task Re-scheduling ...

8th International Conference on Logistics and Systems Engineering 2018

作者： Xie, Ping He, Yongming Wang, Pei Sun, Kai Wang, Lin China Aerospace Academy of Systems Science and Engineering Beijing China College of System Engineering National University of Defense Technology Changsha China Unit 75831 Guangzhou Guangdong510510 China Research Academic Office National University of Defense Technology Changsha China Department of Equipment Support Refabrication Army Academy Amoured Forces Changsha China

ISBN: (纸本)9781921712685

The development of earth observation satellite technology and the soaring demands of users have promoted the great changes in the satellite management and control process. Obviously, the way of ground-based control can hardly meet the users' increasing requirements of timeliness and reliability. The idea of autonomous re-scheduling paves a path for addressing the above issue, in which re-scheduling method is the core technique. This paper focuses on autonomous task re-scheduling problem rather than traditional satellite task scheduling problem. Suppose that the satellite deals with only one task at a time and the computational resources onboard are limited. Considering the time cost and space cost on the satellite, a model of autonomous task re-planning problem is established and an efficient heuristic re-scheduling method is proposed. We thoroughly illustrate the rationality of the algorithm. Then, extensive experiments are carried out, and the results of the proposed methods are compared with commonly used methods in engineering practice. © 2019 Proceedings of the 8th International Conference on Logistics and Systems Engineering 2018. All rights reserved.

关键词： nonlinear programming

A Study of One-Parameter Regularization Methods for Mathematical Programs with Vanishing Constraints

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arXiv 2020年

作者： Hoheisel, Tim Pablos, Blanca Pooladian, Aram-Alexandre Schwartz, Alexandra Steverango, Luke McGill University Department of Mathematics and Statistics 805 Sherbrooke Street West MontrealH3A 0B9 Canada University of the Armed Forces Werner-Heisenberg-Weg 39 Neubiberg85577 Germany Technical University of Darmstadt Dolivostraße 15 Darmstadt64293 Germany Queen’s University Department of Mathematics and Statistics 48 University Ave. KingstonONK7L 3N6 Canada

Mathematical programs with vanishing constraints (MPVCs) are a class of nonlinear optimization problems with applications to various engineering problems such as truss topology design and robot motion planning. MPVCs are difficult problems from both a theoretical and numerical perspective: the combinatorial nature of the vanishing constraints often prevents standard constraint qualifications and optimality conditions from being attained;moreover, the feasible set is inherently nonconvex, and often has no interior around points of interest. In this paper, we therefore study and compare four regularization methods for the numerical solution of MPVCS. Each method depends on a single regularization parameter, which is used to embed the original MPVC into a sequence of standard nonlinear programs. Convergence results for these methods based on both exact and approximate stationary of the subproblems are established under weak assumptions. The improved regularity of the subproblems is studied by providing sufficient conditions for the existence of KKT multipliers. Numerical experiments, based on applications in truss topology design and an optimal control problem from aerothermodynamics, complement the theoretical analysis and comparison of the regularization methods. The computational results highlight the benefit of using regularization over applying a standard solver directly, and they allow us to identify two promising regularization schemes. Copyright © 2020, The Authors. All rights reserved.

关键词： nonlinear programming

On degenerate doubly nonnegative projection problems

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arXiv 2020年

作者： Cui, Ying Liang, Ling Sun, Defeng Toh, Kim-Chuan Department of Industrial and Systems Engineering University of Minnesota Minneapolis United States Department of Mathematics National University of Singapore Singapore Singapore Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Hong Kong Department of Mathematics Institute of Operations Research and Analytics National University of Singapore Singapore Singapore

The doubly nonnegative (DNN) cone, being the set of all positive semidefinite matrices whose elements are nonnegative, is a popular approximation of the computationally intractable completely positive cone. The major difficulty for implementing a Newton-type method to compute the projection of a given large scale matrix onto the DNN cone lies in the possible failure of the constraint nondegeneracy, a generalization of the linear independence constraint qualification for nonlinear programming. Such a failure results in the singularity of the Jacobian of the nonsmooth equation representing the Karush-Kuhn-Tucker optimality condition that prevents the semismooth Newton-CG method from solving it with a desirable convergence rate. In this paper, we overcome the aforementioned difficulty by solving a sequence of better conditioned nonsmooth equations generated by the augmented Lagrangian method (ALM) instead of solving one above mentioned singular equation. By leveraging on the metric subregularity of the normal cone associated with the positive semidefinite cone, we derive sufficient conditions to ensure the dual quadratic growth condition of the underlying problem, which further leads to the asymptotically superlinear convergence of the proposed ALM. Numerical results on difficult randomly generated instances and from the semidefinite programming library are presented to demonstrate the efficiency of the algorithm for computing the DNN projection to a very high *** Codes 90C06, 90C22, 90C25 Copyright © 2020, The Authors. All rights reserved.

关键词： nonlinear programming