Dissertations / Theses on the topic 'Second-Order Cone Programming'
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Okuno, Takayuki. "Studies on Algorithms for Solving Generalized Second-Order Cone Programming Problems." 京都大学 (Kyoto University), 2013. http://hdl.handle.net/2433/174846.
Full textChen, Jein-Shan. "Merit functions and nonsmooth functions for the second-order cone complementarity problem /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/5782.
Full textCAMARGO, JULIA DE TOLEDO. "THREE DIMENSIONAL LIMIT ANALYSIS USING SECOND ORDER CONE PROGRAMMING APPLIED TO SLOPE STABILITY." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=26876@1.
Full textCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
FUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
Visando avaliar uma ferramenta numérica efetiva para resolução de problemas de estabilidade tridimensionais, a análise limite numérica foi estudada neste trabalho. Sua abordagem numérica requer o uso tanto do método dos elementos finitos quanto de programação matemática. Isto porque os teoremas da plasticidade, base da análise limite, podem ser colocados como problemas de otimização. No teorema do limite inferior, por exemplo, se deseja maximizar o fator de colapso, com o solo sujeito a condições de equilíbrio e ao critério de ruptura. O critério de ruptura utilizado foi o de Drucker-Prager. Neste trabalho, fez-se uso da programação cônica quadrática, conhecida por possibilitar a resolução de problemas de grande escala com muita eficiência. Empregou-se, para tanto, o solver Mosek. Além de ser possível determinar o fator de colapso, também se desenvolveu um método para calcular o fator de segurança da encosta. Ele reduz sucessivamente os parâmetros de resistência do solo, através do método de Newton-Raphson. Em casos de geometrias mais complexas, a formulação do problema teve que ser modificada. Uma força horizontal fictícia foi adicionada na condição de equilíbrio e unicamente ela foi majorada com o fator de colapso. Foi apenas através desta formulação que se pode simular a estabilidade de solos submetidos ao efeito de poropressão. A análise de fluxo foi simulada a parte no programa de elementos finitos desenvolvido por Miqueletto (2007). A resistência do solo depende dos valores de poropressão, que caracterizam os solos como saturados ou não saturados.
Numerical limit analysis was studied in order to evaluate an effective numerical procedure to solve three-dimensional slope stability problems. This numerical approach utilizes finite element method and mathematical programming. Mathematical programming is needed because the plasticity theorems, basic theorems for limit analysis, can be cast as optimization problems. The lower bound theorem consists of finding the maximum collapse multiplier that will lead the soil to the imminence of collapse. The soil will still be restricted to equilibrium conditions and the yield criterion will have to be satisfied everywhere. Drucker- Prager was the yield criterion chosen. In this thesis, the optimization problem is reformulated as a second order cone programming (SOCP). SOCP is known to solve large-scale problems with great computational efficiency and we used the solver Mosek. The model calculates not only the collapse multiplier, but also the safety factor for the slope. A strength reduction scheme was proposed, based on the Newton-Raphson method. For complex geometries cases, a novel formulation was developed. A fictitious horizontal force was added at the equilibrium equation and uniquely this force was increased by the multiplier factor. It was only through this reformulation that it was possible to assess stability of slopes subjected to porepressure effects. The groundwater flow was simulated separately in a finite element program developed by Miqueletto (2007). The soil strength depends on porepressure values, which define soils as saturated or unsaturated.
Ciria, Suárez Héctor 1979. "Computation of upper and lower bounds in limit analysis using second-order cone programming and mesh adaptivity." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/16655.
Full textIncludes bibliographical references (p. 109-111).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Limit analysis is relevant in many practical engineering areas such as the design of mechanical structures or the analysis of soil mechanics. Assuming a rigid, perfectly-plastic solid subject to a static load distribution, the problem of limit analysis consists of finding the minimum multiple of this load distribution that will cause the body to collapse. This collapse multiplier results from solving an infinite dimensional saddle point problem, where the internal work rate is maximized over an admissible set of stresses -defined by a yield condition- and minimized over the linear space of kinematically admissible velocities for which the external work rate equals the unity. When strong duality is applied to this saddle point problem, the well-known convex (and equivalent) static and kinematic principles of limit analysis arise. In this thesis, an efficient procedure to compute strict upper and lower bounds for the exact collapse multiplier is presented, with a formulation that explicitly considers the exact convex yield condition. The approach consists of two main steps. First, the continuous problem, under the form of the static principle, is discretized twice (one per bound) by means of different combinations of finite element spaces for the stresses and velocities. For each discretization, the interpolation spaces are chosen so that the attainment of an upper or a lower bound is guaranteed. The second step consists of solving the resulting discrete nonlinear optimization problems. Towards this end, they are reformulated into the canonical form of Second-order Cone Programs, which allows for the use of primal-dual interior point methods that optimally exploit the convexity and duality properties of the limit analysis
(cont.) model and guarantee global convergence to the optimal solutions. To exploit the fact that collapse mechanisms are typically highly localized, a novel method for adaptive meshing is introduced based on local bound gap measures and not on heuristic estimates. The method decomposes the total bound gap as the sum of positive elemental contributions from each element in the mesh, and refines only those elements which are responsible for the majority of the numerical error. Finally, stand-alone computational certificates that allow the bounds to be verified independently, without recourse to the original computer program, are also provided. This removes the uncertainty about the reliability of the results, which frequently undermines the utility of computational simulations. The efficiency of the methodology proposed is illustrated with several applications in plane stress and plane strain, demonstrating that it can be used in complex, realistic problems as a supplement to other models.
by Héctor Ciria Suárez.
S.M.
Mohammad, Salimian. "A Mixed Integer Second Order Cone Programming Reformulation For A Congested Location And Capacity Allocation Problem On A Supply Chain Network." Master's thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615407/index.pdf.
Full textBornhorst, Nils [Verfasser], Marius [Akademischer Betreuer] Pesavento, Martin [Akademischer Betreuer] Haardt, Anja [Akademischer Betreuer] Klein, and Sebastian [Akademischer Betreuer] Schöps. "Energy-Efficient Distributed Multicast Beamforming Using Iterative Second-Order Cone Programming / Nils Bornhorst. Betreuer: Marius Pesavento ; Martin Haardt ; Anja Klein ; Sebastian Schöps." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2015. http://d-nb.info/1110980922/34.
Full textChen, Jieqiu. "Convex relaxations in nonconvex and applied optimization." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/654.
Full textKim, Jae-Hak, and Jae-Hak Kim@anu edu au. "Camera Motion Estimation for Multi-Camera Systems." The Australian National University. Research School of Information Sciences and Engineering, 2008. http://thesis.anu.edu.au./public/adt-ANU20081211.011120.
Full textTerrade, Benjamin. "Evaluation structurale des murs de soutènement en maçonnerie." Thesis, Paris Est, 2017. http://www.theses.fr/2017PESC1203/document.
Full textWherever stone is readily available, we encounter stone masonry buildings. Depending on customs or dedicated use, the blocks are used raw, lightly faced or perfectly cut, with or without the use of mortar. Althougth concrete has replaced masonry in new construction for some decades, the better part of the French built heritage is made of masonry, an heritage we are responsible for. This works aims at contributing to create a reliable scientific frame for that purpose. This thesis uses the yield design theory alongside with homogenisation techniques to study the stability of stone masonry earth retaining walls. First, we provide an analytical tool suitable for designing new structures or assessing the stability of existing ones that are still in good shape. Should it be needed, this tools allows for the design of a strengthening solution based on soil-nailing. Then, we implement it in a finite element code to give it the versatility required to study unconventionnal structures or structures badly damaged. We then present several experimental campaigns aiming at validating the proposed tools
Coutinho, Walton Pereira. "Um algoritmo branch-and-bound para o problema do caixeiro viajante suficientemente próximo." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/5268.
Full textCoordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This research deals with the Close-Enough Traveling Salesman Problem, a variant of the Traveling Salesman Problem wich has several applicatios in logistics. In the Close-Enough Traveling Salesman Problem, rather than visiting the vertex (customer) itself, the salesman must visit a specific region containing such vertex. To solve this problem, we propose a simple yet effective exact algorithm, based on Branch-and-Bound and Second Order Cone Programming. The proposed algorithm was tested in 824 instances suggested in the literature. Optimal solutions are obtained for open problems with up to a thousand vertices. We consider both instances in the two- and three-dimensional space.
Esta pesquisa trata do Problema do Caixeiro Viajante Suficientemente Próximo, uma variante do Problema do Caixeiro Viajante que possui diversas aplicações em logística. No Problema do Caixeiro Viajante Suficientemente Próximo, ao invés de visitar o próprio vértice (cliente), o caixeiro deve visitar uma região especifica contendo este vértice. Para resolver este problema, é proposto um algoritmo exato, simples e efetivo, baseado em branch-and-bound e Programação Cônica de Segunda Ordem. O algoritmo proposto foi testado em 824 instâncias sugeridas na literatura. Soluções ótimas foram obtidas para instâncias com até mil vértices. Foram consideradas instâncias nos espaços bi e tridimensional.
Pham, Anh Tu. "Détermination numérique des propriétés de résistance de roches argileuses." Thesis, Paris Est, 2017. http://www.theses.fr/2017PESC1237/document.
Full textThe strength capacities of Callovo-Oxfordian (COx) argillite which is a potential host rock for the deep underground repository of high-level radioactive waste in France are investigated. At a micro-scale, micro-pores can be observed in the matrix. A first strength homogenization step has been performed in order to evaluate the matrix strength criteria. The microstructure analysis of this material at some hundreds of micromet scale, referred at meso-scale, shows a clay matrix and a random distribution of mineral inclusions (quartz and calcite).Aiming to the determination of COx argillite strength domain, an FEM numerical tool has been developed in the context of the elastoplastic behavior of the matrix. Several morphological patterns of the representative elementary volume have been considered and subjected to an incremental loading in periodic conditions until collapse occurs. As a result of such elastoplastic calculation, one point of the boundary of the strength domain is obtained. The latter then could be reached by successive elastoplastic calculations.As an alternative to direct elastoplastic simulations, kinematic and static approaches of limit analysis are performed. The stress-based (static approach) and the velocity-based (kinematic approach) finite element method are used to develop a numerical tool able to derive a lower bound and upper bound of strength domain, respectively
Cheng, Jianqiang. "Stochastic Combinatorial Optimization." Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112261.
Full textIn this thesis, we studied three types of stochastic problems: chance constrained problems, distributionally robust problems as well as the simple recourse problems. For the stochastic programming problems, there are two main difficulties. One is that feasible sets of stochastic problems is not convex in general. The other main challenge arises from the need to calculate conditional expectation or probability both of which are involving multi-dimensional integrations. Due to the two major difficulties, for all three studied problems, we solved them with approximation approaches.We first study two types of chance constrained problems: linear program with joint chance constraints problem (LPPC) as well as maximum probability problem (MPP). For both problems, we assume that the random matrix is normally distributed and its vector rows are independent. We first dealt with LPPC which is generally not convex. We approximate it with two second-order cone programming (SOCP) problems. Furthermore under mild conditions, the optimal values of the two SOCP problems are a lower and upper bounds of the original problem respectively. For the second problem, we studied a variant of stochastic resource constrained shortest path problem (called SRCSP for short), which is to maximize probability of resource constraints. To solve the problem, we proposed to use a branch-and-bound framework to come up with the optimal solution. As its corresponding linear relaxation is generally not convex, we give a convex approximation. Finally, numerical tests on the random instances were conducted for both problems. With respect to LPPC, the numerical results showed that the approach we proposed outperforms Bonferroni and Jagannathan approximations. While for the MPP, the numerical results on generated instances substantiated that the convex approximation outperforms the individual approximation method.Then we study a distributionally robust stochastic quadratic knapsack problems, where we only know part of information about the random variables, such as its first and second moments. We proved that the single knapsack problem (SKP) is a semedefinite problem (SDP) after applying the SDP relaxation scheme to the binary constraints. Despite the fact that it is not the case for the multidimensional knapsack problem (MKP), two good approximations of the relaxed version of the problem are provided which obtain upper and lower bounds that appear numerically close to each other for a range of problem instances. Our numerical experiments also indicated that our proposed lower bounding approximation outperforms the approximations that are based on Bonferroni's inequality and the work by Zymler et al.. Besides, an extensive set of experiments were conducted to illustrate how the conservativeness of the robust solutions does pay off in terms of ensuring the chance constraint is satisfied (or nearly satisfied) under a wide range of distribution fluctuations. Moreover, our approach can be applied to a large number of stochastic optimization problems with binary variables.Finally, a stochastic version of the shortest path problem is studied. We proved that in some cases the stochastic shortest path problem can be greatly simplified by reformulating it as the classic shortest path problem, which can be solved in polynomial time. To solve the general problem, we proposed to use a branch-and-bound framework to search the set of feasible paths. Lower bounds are obtained by solving the corresponding linear relaxation which in turn is done using a Stochastic Projected Gradient algorithm involving an active set method. Meanwhile, numerical examples were conducted to illustrate the effectiveness of the obtained algorithm. Concerning the resolution of the continuous relaxation, our Stochastic Projected Gradient algorithm clearly outperforms Matlab optimization toolbox on large graphs
Talina, Bernardo Júdice Franqueira Cotrim. "Quadratic programming versus second order con programming in portfolio optimization." Master's thesis, 2016. http://hdl.handle.net/10362/16803.
Full textBornhorst, Nils. "Energy-Efficient Distributed Multicast Beamforming Using Iterative Second-Order Cone Programming." Phd thesis, 2015. https://tuprints.ulb.tu-darmstadt.de/4387/1/Dissertation_Bornhorst_Nils.pdf.
Full textChen, I.-ching, and 陳怡靜. "Support vector regression with noise by using second-order cone programming." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/11385402094271423959.
Full text義守大學
電機工程學系碩士班
96
In this thesis, the regression model establishment is made by support vector machine. And we use an algorithm of second-order cone programming (SOCP) to solve the problem of support vector regression with noise data. We can transform the support vector regression with noisy data problem into the SOCP problem by the operation of mathematical. After the transformation, merit function is applied to solve the SOCP problems. The SOCP algorithm could be applied in many engineering problems such as the filter design, robust control and some optimization problems. Computation results are presented on both synthetic problems and real-world problems, in which we discuss the uncertainty and mean square error values. From the computation results we realize that increase of uncertainty would also certainty the accuracy of prediction.
Toh, Kim Chuan, Zhi Cai, and Robert M. Freund. "Solving symmetric indefinite systems in an interior-point method for second order cone programming." 2002. http://hdl.handle.net/1721.1/4016.
Full textSingapore-MIT Alliance (SMA)
Wu, Xiao-Ren, and 吳孝仁. "Neural Network Approach for Nonlinear Complementarity Problem and Quadratic Programming with Second-Order Cone Constraints." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/ea44k2.
Full text國立臺灣師範大學
數學系
105
This dissertation focuses on two types of optimization problems, nonlinear complementarity problem (NCP for short) and quadratic programming with second-order cone constraints (SOCQP for short). Based on NCP-function and SOC-complementarity function, we propose suitable neural networks for each of them, respectively. For the NCP-function, we propose new one which is the generalization of natural residual function for NCP. It is a discrete generalization of natural residual function phinr, denoted as phinrp. Besides being a NCP-function, we also show its twice dierentiability and present the geometric view. In addition, we utilize neural network approach to solving nonlinear complementarity problems and quadratic programming problems with second-order cone constraints. By building neural networks based on dierent families of smooth NCP or SOCCP-functions. Our goal is to study the stability of the equilibrium with respect to dierent neural network models. Asymptotical stability are built in most neural network models. Under suitable conditions, we show the equilibrium being exponentially stable. Finally, the simulation results are reported to demonstrate the effectiveness of the proposed neural network.
Han, Deren. "Global Optimization with Polynomials." 2003. http://hdl.handle.net/1721.1/3883.
Full textSingapore-MIT Alliance (SMA)
Zhang, Xue. "Particle finite element method in geomechanics." Thesis, 2014. http://hdl.handle.net/1959.13/1055070.
Full textDespite the wide application of the finite element method (FEM) in geotechnical engineering, the numerical analysis usually stops at the point when soil flow occurs and results in overall `failure'. In many cases, the so-called failure only represents a specific time point of the deformation process and the soil flow itself is of interest as well. A typical example is a landslide in which a transition of the soil behaviour is experienced from solid-like to liquid-like, and then back to solid-like. For such problems, a correct understanding of the triggering mechanism is important. However, the prediction of the sliding process as well as the estimation of the final deposit are also of great concern. Unfortunately, the traditional Lagrangian FEM cannot handle problems involving both solid-like and liquid-like behaviour. This is to a large extent, due to the following two issues: (1) Severe mesh distortion and boundary evolution as a result of large changes in geometry. (2) Difficulties in solving the highly nonlinear and non-smooth discrete governing equations in an efficient and robust manner. In this thesis, a new continuum approach that addresses the above two issues explicitly is proposed for handling problems involving the solid-liquid transitional behaviour in geomechanics. More specifically, the first issue is solved via the so-called Particle Finite Element Method (PFEM) originally proposed for the solution of fluid dynamics problems involving free surfaces. The key feature of the PFEM is that mesh nodes are treated as a cloud of particles which can move freely and even separate from the domain to which they originally belong. At each time step, the computational domain is detected based on those particles; then, the conventional FEM is used to solve the problem on the identified domain. Regarding the second issue, mathematical programming formulations for the dynamic analysis of elastoplastic behaviour are developed with a wide utilisation of the Hellinger-Reissner variational theorem. The resulting formulations can be cast as a second-order cone program and solved via appropriate optimization methods. Unlike the conventional Newton-Raphson based FE scheme, the convergence of the solution of the scheme developed is guaranteed regardless of the quality of the initial solution. Formulations for both plane strain and axisymmetric problems are developed. Moreover, the contact between deformable bodies and rigid boundaries is also taken into account. A number of challenging problems in plane strain cases are solved successfully, which demonstrates the capabilities of the proposed approach. Furthermore, the approach is used to reproduce laboratory tests involving the collapse of axisymmetric granular columns. A quantitative comparison between the simulated results and the existing experimental data is conducted. Finally, an actual natural disaster event, the Yangbaodi landslide, is considered and analysed in some detail.
(5930891), Benjamin M. Tackett. "REAL-TIME TRAJECTORY OPTIMIZATION BY SEQUENTIAL CONVEX PROGRAMMING FOR ONBOARD OPTIMAL CONTROL." Thesis, 2021.
Find full textKim, Jae-Hak. "Camera Motion Estimation for Multi-Camera Systems." Phd thesis, 2008. http://hdl.handle.net/1885/49364.
Full textIsmailova, Darya. "Localization algorithms for passive sensor networks." Thesis, 2016. http://hdl.handle.net/1828/7747.
Full textGraduate
0544
ismailds@uvic.ca
Jagarlapudi, Saketha Nath. "Learning Algorithms Using Chance-Constrained Programs." Thesis, 2008. http://hdl.handle.net/2005/733.
Full text