Relevant bibliographies by topics / Nonconvex programming

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Nonconvex programming'

Author: Grafiati
Published: 4 June 2021
Last updated: 31 January 2023

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Journal articles on the topic "Nonconvex programming"

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Falk, James E., and Ferenc Forgo. "Nonconvex Programming." Mathematics of Computation 53, no. 187 (July 1989): 449. http://dx.doi.org/10.2307/2008379.

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Mukai, Hiro. "Nonconvex programming." European Journal of Operational Research 42, no. 1 (September 1989): 105–6. http://dx.doi.org/10.1016/0377-2217(89)90064-7.

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Jiao, Hongwei, and Yongqiang Chen. "A Global Optimization Algorithm for Generalized Quadratic Programming." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/215312.

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We present a global optimization algorithm for solving generalized quadratic programming (GQP), that is, nonconvex quadratic programming with nonconvex quadratic constraints. By utilizing a new linearizing technique, the initial nonconvex programming problem (GQP) is reduced to a sequence of relaxation linear programming problems. To improve the computational efficiency of the algorithm, a range reduction technique is employed in the branch and bound procedure. The proposed algorithm is convergent to the global minimum of the (GQP) by means of the subsequent solutions of a series of relaxation linear programming problems. Finally, numerical results show the robustness and effectiveness of the proposed algorithm.
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Scholtes, Stefan. "Nonconvex Structures in Nonlinear Programming." Operations Research 52, no. 3 (June 2004): 368–83. http://dx.doi.org/10.1287/opre.1030.0102.

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Pardalos, Panos M., and G. M. Guisewite. "Parallel computing in nonconvex programming." Annals of Operations Research 43, no. 2 (February 1993): 87–107. http://dx.doi.org/10.1007/bf02024487.

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Antczak, Tadeusz. "Sufficient optimality conditions for semi-infinite multiobjective fractional programming under (Ф,ρ)-V-invexity and generalized (Ф,ρ)-V-invexity." Filomat 30, no. 14 (2016): 3649–65. http://dx.doi.org/10.2298/fil1614649a.

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A new class of nonconvex smooth semi-infinite multiobjective fractional programming problems with both inequality and equality constraints is considered. We formulate and establish several parametric sufficient optimality conditions for efficient solutions in such nonconvex vector optimization problems under (?,?)-V-invexity and/or generalized (?,?)-V-invexity hypotheses. With the reference to the said functions, we extend some results of efficiency for a larger class of nonconvex smooth semi-infinite multiobjective programming problems in comparison to those ones previously established in the literature under other generalized convexity notions. Namely, we prove the sufficient optimality conditions for such nonconvex semi-infinite multiobjective fractional programming problems in which not all functions constituting them have the fundamental property of convexity, invexity and most generalized convexity notions.
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KUMAR, NARENDER, R. K. BUDHRAJA, and APARNA MEHRA. "APPROXIMATE EFFICIENCY FOR n-SET MULTIOBJECTIVE FRACTIONAL PROGRAMMING." Asia-Pacific Journal of Operational Research 21, no. 02 (June 2004): 197–206. http://dx.doi.org/10.1142/s0217595904000199.

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In this paper, we introduce new concepts of ε-weak efficient solutions and ε-efficient solutions for a nonconvex multiobjective fractional programming problem involving n-set functions. Using an ε-parametric approach and a new theorem of alternative for nonconvex n-set functions, some necessary and sufficient conditions for ε-approximate solutions are derived
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Moloshnyuk, A. N. "A duality relation in nonconvex programming." Journal of Soviet Mathematics 41, no. 3 (May 1988): 1050–53. http://dx.doi.org/10.1007/bf01103261.

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Forsgren, Anders. "Optimality conditions for nonconvex semidefinite programming." Mathematical Programming 88, no. 1 (June 2000): 105–28. http://dx.doi.org/10.1007/pl00011370.

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Antczak, Tadeusz. "Saddle point criteria in semi-infinite minimax fractional programming under (Φ,ρ)-invexity." Filomat 31, no. 9 (2017): 2557–74. http://dx.doi.org/10.2298/fil1709557a.

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Semi-infinite minimax fractional programming problems with both inequality and equality constraints are considered. The sets of parametric saddle point conditions are established for a new class of nonconvex differentiable semi-infinite minimax fractional programming problems under(?,?)-invexity assumptions. With the reference to the said concept of generalized convexity, we extend some results of saddle point criteria for a larger class of nonconvex semi-infinite minimax fractional programming problems in comparison to those ones previously established in the literature.
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Dissertations / Theses on the topic "Nonconvex programming"

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Vielma, Centeno Juan Pablo. "Mixed integer programming approaches for nonlinear and stochastic programming." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29624.

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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010.
Committee Chair: Nemhauser, George; Committee Co-Chair: Ahmed, Shabbir; Committee Member: Bill Cook; Committee Member: Gu, Zonghao; Committee Member: Johnson, Ellis. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Chen, Jieqiu. "Convex relaxations in nonconvex and applied optimization." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/654.

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Traditionally, linear programming (LP) has been used to construct convex relaxations in the context of branch and bound for determining global optimal solutions to nonconvex optimization problems. As second-order cone programming (SOCP) and semidefinite programming (SDP) become better understood by optimization researchers, they become alternative choices for obtaining convex relaxations and producing bounds on the optimal values. In this thesis, we study the use of these convex optimization tools in constructing strong relaxations for several nonconvex problems, including 0-1 integer programming, nonconvex box-constrained quadratic programming (BoxQP), and general quadratic programming (QP). We first study a SOCP relaxation for 0-1 integer programs and a sequential relaxation technique based on this SOCP relaxation. We present desirable properties of this SOCP relaxation, for example, this relaxation cuts off all fractional extreme points of the regular LP relaxation. We further prove that the sequential relaxation technique generates the convex hull of 0-1 solutions asymptotically. We next explore nonconvex quadratic programming. We propose a SDP relaxation for BoxQP based on relaxing the first- and second-order KKT conditions, where the difficulty and contribution lie in relaxing the second-order KKT condition. We show that, although the relaxation we obtain this way is equivalent to an existing SDP relaxation at the root node, it is significantly stronger on the children nodes in a branch-and-bound setting. New advance in optimization theory allows one to express QP as optimizing a linear function over the convex cone of completely positive matrices subject to linear constraints, referred to as completely positive programming (CPP). CPP naturally admits strong semidefinite relaxations. We incorporate the first-order KKT conditions of QP into the constraints of QP, and then pose it in the form of CPP to obtain a strong relaxation. We employ the resulting SDP relaxation inside a finite branch-and-bound algorithm to solve the QP. Comparison of our algorithm with commercial global solvers shows potential as well as room for improvement. The remainder is devoted to new techniques for solving a class of large-scale linear programming problems. First order methods, although not as fast as second-order methods, are extremely memory efficient. We develop a first-order method based on Nesterov's smoothing technique and demonstrate the effectiveness of our method on two machine learning problems.
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Vandenbussche, Dieter. "Polyhedral approaches to solving nonconvex quadratic programs." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/23385.

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Wang, Hongjie. "Global Optimization of Nonconvex Factorable Programs with Applications to Engineering Design Problems." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36823.

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The primary objective of this thesis is to develop and implement a global optimization algorithm to solve a class of nonconvex programming problems, and to test it using a collection of engineering design problem applications.The class of problems we consider involves the optimization of a general nonconvex factorable objective function over a feasible region that is restricted by a set of constraints, each of which is defined in terms of nonconvex factorable functions. Such problems find widespread applications in production planning, location and allocation, chemical process design and control, VLSI chip design, and numerous engineering design problems. This thesis offers a first comprehensive methodological development and implementation for determining a global optimal solution to such factorable programming problems. To solve this class of problems, we propose a branch-and-bound approach based on linear programming (LP) relaxations generated through various approximation schemes that utilize, for example, the Mean-Value Theorem and Chebyshev interpolation polynomials, coordinated with a {em Reformulation-Linearization Technique} (RLT). The initial stage of the lower bounding step generates a tight, nonconvex polynomial programming relaxation for the given problem. Subsequently, an LP relaxation is constructed for the resulting polynomial program via a suitable RLT procedure. The underlying motivation for these two steps is to generate a tight outer approximation of the convex envelope of the objective function over the convex hull of the feasible region. The bounding step is thenintegrated into a general branch-and-bound framework. The construction of the bounding polynomials and the node partitioning schemes are specially designed so that the gaps resulting from these two levels of approximations approach zero in the limit, thereby ensuring convergence to a global optimum. Various implementation issues regarding the formulation of such tight bounding problems using both polynomial approximations and RLT constructs are discussed. Different practical strategies and guidelines relating to the design of the algorithm are presented within a general theoretical framework so that users can customize a suitable approach that takes advantage of any inherent special structures that their problems might possess. The algorithm is implemented in C++, an object-oriented programming language. The class modules developed for the software perform various functions that are useful not only for the proposed algorithm, but that can be readily extended and incorporated into other RLT based applications as well. Computational results are reported on a set of fifteen engineering process control and design test problems from various sources in the literature. It is shown that, for all the test problems, a very competitive computational performance is obtained. In most cases, the LP solution obtained for the initial node itself provides a very tight lower bound. Furthermore, for nine of these fifteen problems, the application of a local search heuristic based on initializing the nonlinear programming solver MINOS at the node zero LP solution produced the actual global optimum. Moreover, in finding a global optimum, our algorithm discovered better solutions than the ones previously reported in the literature for two of these test instances.
Master of Science
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Hu, Sha S. M. Massachusetts Institute of Technology. "Semidefinite relaxation based branch-and-bound method for nonconvex quadratic programming." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/39217.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.
Includes bibliographical references (leaves 73-75).
In this thesis, we use a semidefinite relaxation based branch-and-bound method to solve nonconvex quadratic programming problems. Firstly, we show an interval branch-and-bound method to calculate the bounds for the minimum of bounded polynomials. Then we demonstrate four SDP relaxation methods to solve nonconvex Box constrained Quadratic Programming (BoxQP) problems and the comparison of the four methods. For some lower dimensional problems, SDP relaxation methods can achieve tight bounds for the BoxQP problem; whereas for higher dimensional cases (more than 20 dimensions), the bounds achieved by the four Semidefinite programming (SDP) relaxation methods are always loose. To achieve tight bounds for higher dimensional BoxQP problems, we combine the branch-and-bound method and SDP relaxation method to develop an SDP relaxation based branch-and-bound (SDPBB) method. We introduce a sensitivity analysis method for the branching process of SDPBB. This sensitivity analysis method can improve the convergence speed significantly.
(cont.) Compared to the interval branch-and-bound method and the global optimization software BARON, SDPBB can achieve better bounds and is also much more efficient. Additionally, we have developed a multisection algorithm for SDPBB and the multisection algorithm has been parallelized using Message Passing Interface (MPI). By parallelizing the program, we can significantly improve the speed of solving higher dimensional BoxQP problems.
by Sha Hu.
S.M.
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Mankau, Jan Peter. "A Nonsmooth Nonconvex Descent Algorithm." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-217556.

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In many applications nonsmooth nonconvex energy functions, which are Lipschitz continuous, appear quite naturally. Contact mechanics with friction is a classic example. A second example is the 1-Laplace operator and its eigenfunctions. In this work we will give an algorithm such that for every locally Lipschitz continuous function f and every sequence produced by this algorithm it holds that every accumulation point of the sequence is a critical point of f in the sense of Clarke. Here f is defined on a reflexive Banach space X, such that X and its dual space X' are strictly convex and Clarkson's inequalities hold. (E.g. Sobolev spaces and every closed subspace equipped with the Sobolev norm satisfy these assumptions for p>1.) This algorithm is designed primarily to solve variational problems or their high dimensional discretizations, but can be applied to a variety of locally Lipschitz functions. In elastic contact mechanics the strain energy is often smooth and nonconvex on a suitable domain, while the contact and the friction energy are nonsmooth and have a support on a subspace which has a substantially smaller dimension than the strain energy, since all points in the interior of the bodies only have effect on the strain energy. For such elastic contact problems we suggest a specialization of our algorithm, which treats the smooth part with Newton like methods. In the case that the gradient of the entire energy function is semismooth close to the minimizer, we can even prove superlinear convergence of this specialization of our algorithm. We test the algorithm and its specialization with a couple of benchmark problems. Moreover, we apply the algorithm to the 1-Laplace minimization problem restricted to finitely dimensional subspaces of piecewise affine, continuous functions. The algorithm developed here uses ideas of the bundle trust region method by Schramm, and a new generalization of the concept of gradients on a set. The basic idea behind this gradients on sets is that we want to find a stable descent direction, which is a descent direction on an entire neighborhood of an iteration point. This way we avoid oscillations of the gradients and very small descent steps (in the smooth and in the nonsmooth case). It turns out, that the norm smallest element of the gradient on a set provides a stable descent direction. The algorithm we present here is the first algorithm which can treat locally Lipschitz continuous functions in this generality, up to our knowledge. In particular, large finitely dimensional Banach spaces haven't been studied for nonsmooth nonconvex functions so far. We will show that the algorithm is very robust and often faster than common algorithms. Furthermore, we will see that with this algorithm it is possible to compute reliably the first eigenfunctions of the 1-Laplace operator up to disretization errors, for the first time
In vielen Anwendungen tauchen nichtglatte, nichtkonvexe, Lipschitz-stetige Energie Funktionen in natuerlicher Weise auf. Ein klassische Beispiel bildet die Kontaktmechanik mit Reibung. Ein weiteres Beispiel ist der $1$-Laplace Operator und seine Eigenfunktionen. In dieser Dissertation werden wir ein Abstiegsverfahren angeben, so dass fuer jede lokal Lipschitz-stetige Funktion f jeder Haeufungspunkt einer durch dieses Verfahren erzeugten Folge ein kritischer Punkt von f im Sinne von Clarke ist. Hier ist f auf einem einem reflexiver, strikt konvexem Banachraum definierert, fuer den der Dualraum ebenfalls strikt konvex ist und die Clarkeson Ungleichungen gelten. (Z.B. Sobolevraeume und jeder abgeschlossene Unterraum mit der Sobolevnorm versehen, erfuellt diese Bedingung fuer p>1.) Dieser Algorithmus ist primaer entwickelt worden um Variationsprobleme, bzw. deren hochdimensionalen Diskretisierungen zu loesen. Er kann aber auch fuer eine Vielzahl anderer lokal Lipschitz stetige Funktionen eingesetzt werden. In der elastischen Kontaktmechanik ist die Spannungsenergie oft glatt und nichtkonvex auf einem geeignetem Definitionsbereich, waehrend der Kontakt und die Reibung durch nicht glatte Funktionen modelliert werden, deren Traeger ein Unterraum mit wesentlich kleineren Dimension ist, da alle Punkte im Inneren des Koerpers nur die Spannungsenergie beeinflussen. Fuer solche elastischen Kontaktprobleme schlagen wir eine Spezialisierung unseres Algorithmuses vor, der den glatten Teil mit Newton aehnlichen Methoden behandelt. Falls der Gradient der gesamten Energiefunktion semiglatt in der Naehe der Minimalstelle ist, koennen wir sogar beweisen, dass der Algorithmus superlinear konvergiert. Wir testen den Algorithmus und seine Spezialisierung an mehreren Benchmark Problemen. Ausserdem wenden wir den Algorithmus auf 1-Laplace Minimierungsproblem eingeschraenkt auf eine endlich dimensionalen Unterraum der stueckweise affinen, stetigen Funktionen an. Der hier entwickelte Algorithmus verwendet Ideen des Bundle-Trust-Region-Verfahrens von Schramm, und einen neu entwickelten Verallgemeinerung von Gradienten auf Mengen. Die zentrale Idee hinter den Gradienten auf Mengen ist die, dass wir stabile Abstiegsrichtungen auf einer ganzen Umgebung der Iterationspunkte finden wollen. Auf diese Weise vermeiden wir das Oszillieren der Gradienten und sehr kleine Abstiegsschritte (im glatten, wie im nichtglatten Fall.) Es stellt sich heraus, dass das normkleinste Element dieses Gradienten auf der Umgebung eine stabil Abstiegsrichtung bestimmt. So weit es uns bekannt ist, koennen die hier entwickelten Algorithmen zum ersten Mal lokal Lipschitz-stetige Funktionen in dieser Allgemeinheit behandeln. Insbesondere wurden nichtglatte, nichtkonvexe Funktionen auf derart hochdimensionale Banachraeume bis jetzt nicht behandelt. Wir werden zeigen, dass unser Algorithmus sehr robust und oft schneller als uebliche Algorithmen ist. Des Weiteren, werden wir sehen, dass es mit diesem Algorithmus das erste mal moeglich ist, zuverlaessig die erste Eigenfunktion des 1-Laplace Operators bis auf Diskretisierungsfehler zu bestimmen
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Kleniati, Polyxeni M. "Decomposition schemes for polynomial optimisation, semidefinite programming and applications to nonconvex portfolio decisions." Thesis, Imperial College London, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509792.

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Fraticelli, Barbara M. P. "Semidefinite Cuts and Partial Convexification Techniques with Applications to Continuous Nonconvex Optimization, Stochastic Integer Programming, and Facility Layout Problems." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/27293.

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This dissertation develops efficient solution techniques for general and problem-specific applications within nonconvex optimization, exploiting the constructs of the Reformulation-Linearization Technique (RLT). We begin by developing a technique to enhance general problems in nonconvex optimization through the use of a new class of RLT cuts, called semidefinite cuts. While these cuts are valid for any general problem for which RLT is applicable, we demonstrate their effectiveness in optimizing a nonconvex quadratic objective function over a simplex. Computational results indicate that on average, the semidefinite cuts have reduced the number of nodes in the branch-and-bound tree by a factor of 37.6, while decreasing solution time by a factor of 3.4. The semidefinite cuts have also led to a significant reduction in the optimality gap at termination, in some cases producing optimal solutions for problems that could not be solved using RLT alone. We then narrow our focus to the class of mixed-integer programming (MIP) problems, and develop a modification of Bendersâ decomposition method using concepts from RLT and lift-and-project cuts. This method is particularly motivated by the class of two-stage stochastic programs with integer recourse. The key idea is to design an RLT or lift-and-project cutting plane scheme for solving the subproblems where the cuts generated have right-hand sides that are functions of the first-stage variables. An illustrative example is provided to elucidate the proposed approach. The focus is on developing a first comprehensive finitely convergent extension of Bendersâ methodology for problems having 0-1 mixed-integer subproblems. We next address a specific challenging MIP application known as the facility layout problem, and we significantly improve its formulation through outer-linearization techniques and concepts from disjunctive programming. The enhancements produce a substantial increase in the accuracy of the layout produced, while at the same time, providing a dramatic reduction in computational effort. Overall, the maximum error in department size was reduced from about 6% to nearly zero, while solution time decreased by a factor of 110. Previously unsolved test problems from the literature that had defied even approximate solution methods have been solved to exact optimality using our proposed approach.
Ph. D.
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Yang, Boshi. "A conic optimization approach to variants of the trust region subproblem." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1938.

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The Trust Region Subproblem (TRS), which minimizes a nonconvex quadratic function over the unit ball, is an important subproblem in trust region methods for nonlinear optimization. Even though TRS is a nonconvex problem, it can be solved in polynomial time using, for example, a semidefinite programming (SDP) relaxation. Different variants of TRS have been considered from both theoretical and practical perspectives. In this thesis, we study three variants of TRS and their SDP/conic relaxations. We first study an extended trust region subproblem (eTRS) in which the trust region equals the intersection of the unit ball with M linear cuts. When m = 0, when m = 1, or when m = 2 and the linear cuts are parallel, it is known that the eTRS optimal value equals the optimal value of a particular conic relaxation, which is solvable in polynomial time. However, it is also known that, when m ≥2 and at least two of the linear cuts intersect within the ball, i.e., some feasible point of the eTRS satisfies both linear constraints at equality, then the same conic relaxation may admit a gap with eTRS. We show that the conic relaxation admits no gap for arbitrary M as long as the linear cuts are non-intersecting. We then extend our result to a more general setting. We study an eTRS in which a quadratic function is minimized over a structured nonconvex feasible region: the unit ball with M linear cuts and R hollows. In the special case when m = 0 and r = 1, it is known that the eTRS has a tight polynomial-time solvable conic relaxation. We show that a certain conic relaxation is also tight for general R and M as long as the cuts and hollows satisfy some non-intersecting assumptions that generalize the previous paragraph. Finally, intersecting the feasible region of TRS with a second ellipsoid results in the two-trust-region subproblem (TTRS). Even though TTRS can also be solved in polynomial-time, existing approaches do not provide a concise conic relaxation. We investigate the use of conic relaxation for TTRS. Starting from the basic SDP relaxation of TTRS, which admits a gap, recent research has tightened the basic relaxation using valid second-order-cone (SOC) inequalities. For the special case of TTRS in dimension n=2, we fully characterize the remaining valid inequalities, which can be viewed as strengthened versions of the SOC inequalities just mentioned. We also demonstrate that these valid inequalities can be used computationally even when n > 2 to solve TTRS instances that were previously unsolved using techniques of conic relaxation.
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Cui, Lei. "Topics in image recovery and image quality assessment /Cui Lei." HKBU Institutional Repository, 2016. https://repository.hkbu.edu.hk/etd_oa/368.

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Image recovery, especially image denoising and deblurring is widely studied during the last decades. Variational models can well preserve edges of images while restoring images from noise and blur. Some variational models are non-convex. For the moment, the methods for non-convex optimization are limited. This thesis finds new non-convex optimizing method called difference of convex algorithm (DCA) for solving different variational models for various kinds of noise removal problems. For imaging system, noise appeared in images can show different kinds of distribution due to the different imaging environment and imaging technique. Here we show how to apply DCA to Rician noise removal and Cauchy noise removal. The performance of our experiments demonstrates that our proposed non-convex algorithms outperform the existed ones by better PSNR and less computation time. The progress made by our new method can improve the precision of diagnostic technique by reducing Rician noise more efficiently and can improve the synthetic aperture radar imaging precision by reducing Cauchy noise within. When applying variational models to image denoising and deblurring, a significant subject is to choose the regularization parameters. Few methods have been proposed for regularization parameter selection for the moment. The numerical algorithms of existed methods for parameter selection are either complicated or implicit. In order to find a more efficient and easier way to estimate regularization parameters, we create a new image quality sharpness metric called SQ-Index which is based on the theory of Global Phase Coherence. The new metric can be used for estimating parameters for a various of variational models, but also can estimate the noise intensity based on special models. In our experiments, we show the noise estimation performance with this new metric. Moreover, extensive experiments are made for dealing with image denoising and deblurring under different kinds of noise and blur. The numerical results show the robust performance of image restoration by applying our metric to parameter selection for different variational models.
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Books on the topic "Nonconvex programming"

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Ferenc, Forgó. Nonconvex programming. Budapest: Akadémiai Kiadó, 1988.

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Relaxation and decomposition methods for mixed integer nonlinear programming. Boston, MA: Birkhäuser Verlag, 2005.

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Gao, David Yang. Duality principles in nonconvex systems: Theory, methods, and applications. Dordrecht: Kluwer Academic Publishers, 2000.

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Gao, David Yang. Duality Principles in Nonconvex Systems: Theory, Methods and Applications. Boston, MA: Springer US, 2000.

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Sherali, Hanif D. A reformulation-linearization technique for solving discrete and continuous nonconvex problems. Dordrecht: Kluwer Academic, 1998.

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V, Kalashnikov V., ed. Optimization with multivalued mappings: Theory, applications, and algorithms. New York: Springer, 2006.

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Sherali, Hanif D. A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems. Boston, MA: Springer US, 1999.

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E, Stavroulakis G., ed. Nonconvex optimization in mechanics: Algorithms, heuristics, and engineering applications by the F.E.M. Dordrecht: Kluwer Academic Publishers, 1998.

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Xiaoqi, Yang, ed. Lagrange-type functions in constrained non-convex optimization. Boston: Kluwer Academic Publishers, 2003.

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Bühlmann, Peter. Statistics for High-Dimensional Data: Methods, Theory and Applications. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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Book chapters on the topic "Nonconvex programming"

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Tuy, Hoang. "Nonconvex Quadratic Programming." In Nonconvex Optimization and Its Applications, 277–318. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2809-5_8.

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Tuy, Hoang. "Nonconvex Quadratic Programming." In Springer Optimization and Its Applications, 337–90. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31484-6_10.

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Glover, B. M., and V. Jeyakumar. "Abstract nonsmooth nonconvex programming." In Lecture Notes in Economics and Mathematical Systems, 186–210. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-46802-5_16.

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Horst, Reiner, Panos M. Pardalos, and Nguyen V. Thoai. "Quadratic Programming." In Nonconvex Optimization and Its Applications, 49–107. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-0015-5_2.

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Horst, Reiner, Panos M. Pardalos, and Nguyen V. Thoai. "D.C. Programming." In Nonconvex Optimization and Its Applications, 195–235. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-0015-5_4.

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Bard, Jonathan F. "Linear Programming." In Nonconvex Optimization and Its Applications, 17–75. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2836-1_2.

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Bard, Jonathan F. "Integer Programming." In Nonconvex Optimization and Its Applications, 76–136. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2836-1_3.

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Bard, Jonathan F. "Nonlinear Programming." In Nonconvex Optimization and Its Applications, 137–92. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2836-1_4.

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Du, Ding-Zhu, Panos M. Pardalos, and Weili Wu. "Semidefinite Programming." In Nonconvex Optimization and Its Applications, 201–13. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-5795-8_13.

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Du, Ding-Zhu, Panos M. Pardalos, and Weili Wu. "Linear Programming." In Nonconvex Optimization and Its Applications, 23–40. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-5795-8_2.

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Conference papers on the topic "Nonconvex programming"

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Sakawa, M., and I. Nishizaki. "Interactive fuzzy programming for two-level nonconvex programming problems through the revised GENOCOP III." In Proceedings of 8th International Fuzzy Systems Conference. IEEE, 1999. http://dx.doi.org/10.1109/fuzzy.1999.790174.

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You, Sixiong, and Ran Dai. "Local Optimization of Nonconvex Mixed-Integer Quadratically Constrained Quadratic Programming Problems." In 2020 59th IEEE Conference on Decision and Control (CDC). IEEE, 2020. http://dx.doi.org/10.1109/cdc42340.2020.9304368.

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Wu, Pengxia, Hui Ma, and Julian Cheng. "Sparse Channel Reconstruction With Nonconvex Regularizer via DC Programming for Massive MIMO Systems." In GLOBECOM 2020 - 2020 IEEE Global Communications Conference. IEEE, 2020. http://dx.doi.org/10.1109/globecom42002.2020.9347964.

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Eremeev, A. V., N. N. Tyunin, and A. S. Yurkov. "THE RESEARCH OF ONE PROBLEM NONCONVEX QUADRATIC PROGRAMMING IN SHORTWAVE ANTENNA ARRAY OPTIMIZATION." In V International Scientific and Technical Conference "Radio Engineering, Electronics and Communication". Omsk Scientific-Research Institute of Instrument Engineering, 2019. http://dx.doi.org/10.33286/978-5-6041917-2-9.171-174.

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Xiuyu Wang, Xingwu Jiang, Taishan Yang, and Qinghuai Liu. "The homotopy interior point method for solving a class of nonlinear nonconvex programming problems." In 2010 3rd International Conference on Advanced Computer Theory and Engineering (ICACTE 2010). IEEE, 2010. http://dx.doi.org/10.1109/icacte.2010.5579065.

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He Li, Wang Xiu-yu, Jin Jian-lu, and Qing-huai Liu. "A combined homotopy method for nonconvex multi-objective programming problem with equality and inequality constrains." In 2010 International Conference on Computer, Mechatronics, Control and Electronic Engineering (CMCE 2010). IEEE, 2010. http://dx.doi.org/10.1109/cmce.2010.5609630.

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Li, Hecheng, and Yuping Wang. "A real-binary coded genetic algorithm for solving nonlinear bilevel programming with nonconvex objective functions." In 2011 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2011. http://dx.doi.org/10.1109/cec.2011.5949927.

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Xu, Junyan, Qinghuai Liu, and Zhuang Miao. "A Combined Homotopy Method for Solving a Nonconvex Programming with a Class of Pseudo Cone Condition." In 2011 International Conference on Computational and Information Sciences (ICCIS). IEEE, 2011. http://dx.doi.org/10.1109/iccis.2011.22.

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Sandgren, E., and T. Dworak. "Part Layout Optimization Using a Quadtree Representation." In ASME 1988 Design Technology Conferences. American Society of Mechanical Engineers, 1988. http://dx.doi.org/10.1115/detc1988-0027.

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Abstract:
Abstract A nonlinear programming formulation is developed for minimizing the area required to position a set of pre-defined objects without overlap. The objects consist of polygons with an arbitrary number of edges. Nonconvex polygons are assumed which allows for the modelling of complex parts, including parte with holes. A quadtree representation is formed for each polygon and intersections are determined by traversing quadtrees for the potentially intersecting objects. The design variables are selected to be the x and y location and the rotation for each polygon that is to be positioned. An exterior penalty function method is used to generate the solution to the resulting nonlinear programming problem. A nongradient search technique is used due to the discrete nature of the overlap constraints. Example problems are presented and extensions to other classes of problems are discussed.
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Men, Han, Robert M. Freund, Ngoc C. Nguyen, Joel Saa-Seoane, and Jaime Peraire. "Designing Phononic Crystals With Convex Optimization." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-64694.

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Designing phononic crystals by creating frequency bandgaps is of particular interest in the engineering of elastic and acoustic microstructured materials. Mathematically, the problem of optimizing the frequency bandgaps is often nonconvex, as it requires the maximization of the higher indexed eigenfrequency and the minimization of the lower indexed eigenfrequency. A novel algorithm [1] has been previously developed to reformulate the original nonlinear, nonconvex optimization problem to an iteration-specific semidefinite program (SDP). This algorithm separates two consecutive eigenvalues — effectively maximizing bandgap (or bandwidth) — by separating the gap between two orthogonal subspaces, which are comprised columnwise of “important” eigenvectors associated with the eigenvalues being bounded. By doing so, we avoid the need of computation of eigenvalue gradient by computing the gradient of affine matrices with respect to the decision variables. In this work, we propose an even more efficient algorithm based on linear programming (LP). The new formulation is obtained via approximation of the semidefinite cones by judiciously chosen linear bases, coupled with “delayed constraint generation”. We apply the two convex conic formulations, namely, the semidefinite program and the linear program, to solve the bandgap optimization problems. By comparing the two methods, we demonstrate the efficacy and efficiency of the LP-based algorithm in solving the category of eigenvalue bandgap optimization problems.
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