Relevant bibliographies by topics / Programming (Mathematics) Convex programming

Contents

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

Academic literature on the topic 'Programming (Mathematics) Convex programming'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Programming (Mathematics) Convex programming"

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Ceria, Sebastián, and João Soares. "Convex programming for disjunctive convex optimization." Mathematical Programming 86, no. 3 (December 1, 1999): 595–614. http://dx.doi.org/10.1007/s101070050106.

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Xu, Z. K., and S. C. Fang. "Unconstrained convex programming approach to linear programming." Journal of Optimization Theory and Applications 86, no. 3 (September 1995): 745–52. http://dx.doi.org/10.1007/bf02192167.

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fang, S. C., and H. S. J. Tsao. "An unconstrained convex programming approach to solving convex quadratic programming problems." Optimization 27, no. 3 (January 1993): 235–43. http://dx.doi.org/10.1080/02331939308843884.

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Fang, S. C. "An unconstrained convex programming view of linear programming." ZOR Zeitschrift f� Operations Research Methods and Models of Operations Research 36, no. 2 (March 1992): 149–61. http://dx.doi.org/10.1007/bf01417214.

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Kutateladze, S. S. "Variant of nontandard convex programming." Siberian Mathematical Journal 27, no. 4 (1987): 537–44. http://dx.doi.org/10.1007/bf00969166.

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Jeyakumar, V., and B. Mond. "On generalised convex mathematical programming." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 34, no. 1 (July 1992): 43–53. http://dx.doi.org/10.1017/s0334270000007372.

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AbstractThe sufficient optimality conditions and duality results have recently been given for the following generalised convex programming problem:where the funtion f and g satisfyfor some η: X0 × X0 → ℝnIt is shown here that a relaxation defining the above generalised convexity leads to a new class of multi-objective problems which preserves the sufficient optimality and duality results in the scalar case, and avoids the major difficulty of verifying that the inequality holds for the same function η(. , .). Further, this relaxation allows one to treat certain nonlinear multi-objective fractional programming problems and some other classes of nonlinear (composite) problems as special cases.
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Rajasekera, J. R., and S. C. Fang. "On the convex programming approach to linear programming." Operations Research Letters 10, no. 6 (August 1991): 309–12. http://dx.doi.org/10.1016/0167-6377(91)90001-6.

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Trujillo-Cortez, R., and S. Zlobec. "Bilevel convex programming models." Optimization 58, no. 8 (November 2009): 1009–28. http://dx.doi.org/10.1080/02331930701763330.

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Weir, T. "Programming with semilocally convex functions." Journal of Mathematical Analysis and Applications 168, no. 1 (July 1992): 1–12. http://dx.doi.org/10.1016/0022-247x(92)90185-g.

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Champion, T. "Duality gap in convex programming." Mathematical Programming 99, no. 3 (April 1, 2004): 487–98. http://dx.doi.org/10.1007/s10107-003-0461-z.

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Dissertations / Theses on the topic "Programming (Mathematics) Convex programming"

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Trujillo-Cortez, Refugio. "Stable convex parametric programming and applications." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37856.

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This thesis is a study of stable perturbations in convex programming models. Stability of a general model is introduced as lower semicontinuity of the feasible set mapping. This stability is shown to be equivalent to the Robinson notion of stability and regularity. In the convex case, it is also equivalent to the full-rank Slater condition. Then, the relationships between various point-to-set mappings are studied for convex models and new implications between these mappings are established. Also, local and global optimality of parameters is studied. A new result here is a characterization of locally optimal parameters that does not require stable perturbations. This result is valid, in particular, for convex models with LFS constraints. The value of the model can be improved by one of several new formulations of the marginal value formula.
The results on stability are applied for bilevel convex models and an algorithm for solving these models, based on a marginal value formula, is suggested and then applied to a real-life problem in the petroleum industry.
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Yue, Hongwei. "First-order affine scaling continuous method for convex quadratic programming." HKBU Institutional Repository, 2014. https://repository.hkbu.edu.hk/etd_oa/39.

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We develop several continuous method models for convex quadratic programming (CQP) problems with di.erent types of constraints. The essence of the continuous method is to construct one ordinary di.erential equation (ODE) system such that its limiting equilibrium point corresponds to an optimal solution of the underlying optimization problem. All our continuous method models share the main feature of the interior point methods, i.e., starting from any interior point, all the solution trajectories remain in the interior of the feasible regions. First, we present an a.ne scaling continuous method model for nonnegativity constrained CQP. Under the boundedness assumption of the optimal set, a thorough study on the properties of the ordinary di.erential equation is provided, strong con­vergence of the continuous trajectory of the ODE system is proved. Following the features of this ODE system, a new ODE system for solving box constrained CQP is also presented. Without projection, the whole trajectory will stay inside the box region, and it will converge to an optimal solution. Preliminary simulation results illustrate that our continuous method models are very encouraging in obtaining the optimal solutions of the underlying optimization problems. For CQP in the standard form, the convergence of the iterative .rst-order a.ne scaling algorithm is still open. Under boundedness assumption of the optimal set and nondegeneracy assumption of the constrained region, we discuss the properties of the ODE system induced by the .rst-order a.ne scaling direction. The strong convergence of the continuous trajectory of the ODE system is also proved. Finally, a simple iterative scheme induced from our ODE is presented for find­ing an optimal solution of nonnegativity constrained CQP. The numerical results illustrate the good performance of our continuous method model with this iterative scheme. Keywords: ODE; Continuous method; Quadratic programming; Interior point method; A.ne scaling.
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Yang, Yi. "Sequential convex approximations of chance constrained programming /." View abstract or full-text, 2008. http://library.ust.hk/cgi/db/thesis.pl?IELM%202008%20YANG.

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Dong, Hongbo. "Copositive programming: separation and relaxations." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/2692.

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A large portion of research in science and engineering, as well as in business, concerns one similar problem: how to make things "better”? Once properly modeled (although usually a highly nontrivial task), this kind of questions can be approached via a mathematical optimization problem. Optimal solution to a mathematical optimization problem, when interpreted properly, might corresponds to new knowledge, effective methodology or good decisions in corresponding application area. As already proved in many success stories, research in mathematical optimization has a significant impact on numerous aspects of human life. Recently, it was discovered that a large amount of difficult optimization problems can be formulated as copositive programming problems. Famous examples include a large class of quadratic optimization problems as well as many classical combinatorial optimization problems. For some more general optimization problems, copositive programming provides a way to construct tight convex relaxations. Because of this generality, new knowledge of copositive programs has the potential of being uniformly applied to these cases. While it is provably difficult to design efficient algorithms for general copositive programs, we study copositive programming from two standard aspects, its relaxations and its separation problem. With regard to constructing computational tractable convex relaxations for copositive programs, we develop direct constructions of two tensor relaxation hierarchies for the completely positive cone, which is a fundamental geometric object in copositive programming. We show connection of our relaxation hierarchies with known hierarchies. Then we consider the application of these tensor relaxations to the maximum stable set problem. With regard to the separation problem for copositive programming. We first prove some new results in low dimension of 5 x 5 matrices. Then we show how a separation procedure for this low dimensional case can be extended to any symmetric matrices with a certain block structure. Last but not least, we provide another approach to the separation and relaxations for the (generalized) completely positive cone. We prove some generic results, and discuss applications to the completely positive case and another case related to box-constrained quadratic programming. Finally, we conclude the thesis with remarks on some interesting open questions in the field of copositive programming.
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Dadush, Daniel Nicolas. "Integer programming, lattice algorithms, and deterministic volume estimation." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44807.

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The main subject of this thesis is the development of new geometric tools and techniques for solving classic problems within the geometry of numbers and convex geometry. At a high level, the problems considered in this thesis concern the varied interplay between the continuous and the discrete, an important theme within computer science and operations research. The first subject we consider is the study of cutting planes for non-linear integer programs. Cutting planes have been implemented to great effect for linear integer programs, and so understanding their properties in more general settings is an important subject of study. As our contribution to this area, we show that Chvatal-Gomory closure of any compact convex set is a rational polytope. As a consequence, we resolve an open problem of Schrijver (Ann. Disc. Math. `80) regarding the same question for irrational polytopes. The second subject of study is that of ellipsoidal approximation of convex bodies. Different such notions have been important to the development of fundamental geometric algorithms: e.g. the ellipsoid method for convex optimization (enclosing ellipsoids), or random walk methods for volume estimation (inertial ellipsoids). Here we consider the construction of an ellipsoid with good "covering" properties with respect to a convex body, known in convex geometry as the M-ellipsoid. As our contribution, we give two algorithms for constructing M-ellipsoids, and provide an application to near-optimal deterministic volume estimation in the oracle model. Equipped with this new geometric tool, we move to the study of classic lattice problems in the geometry of numbers, namely the Shortest (SVP) and Closest Vector Problems (CVP). Here we use M-ellipsoid coverings, combined with an algorithm of Micciancio and Voulgaris for CVP in the ℓ₂ norm (STOC `10), to obtain the first deterministic 2^O(ⁿ) time algorithm for the SVP in general norms. Combining this algorithm with a novel lattice sparsification technique, we derive the first deterministic 2^O(ⁿ)(1+1/ϵ)ⁿ time algorithm for (1+ϵ)-approximate CVP in general norms. For the next subject of study, we analyze the geometry of general integer programs. A central structural result in this area is Kinchine's flatness theorem, which states that every lattice free convex body has integer width bounded by a function of dimension. As our contribution, we build on the work Banaszczyk, using tools from lattice based cryptography, to give a new and tighter proof of the flatness theorem. Lastly, combining all the above techniques, we consider the study of algorithms for the Integer Programming Problem (IP). As our main contribution, we give a new 2^O(ⁿ)nⁿ time algorithm for IP, which yields the fastest currently known algorithm for IP and improves on the classic works of Lenstra (MOR `83) and Kannan (MOR `87).
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Potaptchik, Marina. "Portfolio Selection Under Nonsmooth Convex Transaction Costs." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2940.

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We consider a portfolio selection problem in the presence of transaction costs. Transaction costs on each asset are assumed to be a convex function of the amount sold or bought. This function can be nondifferentiable in a finite number of points. The objective function of this problem is a sum of a convex twice differentiable function and a separable convex nondifferentiable function. We first consider the problem in the presence of linear constraints and later generalize the results to the case when the constraints are given by the convex piece-wise linear functions.

Due to the special structure, this problem can be replaced by an equivalent differentiable problem in a higher dimension. It's main drawback is efficiency since the higher dimensional problem is computationally expensive to solve.

We propose several alternative ways to solve this problem which do not require introducing new variables or constraints. We derive the optimality conditions for this problem using subdifferentials. First, we generalize an active set method to this class of problems. We solve the problem by considering a sequence of equality constrained subproblems, each subproblem having a twice differentiable objective function. Information gathered at each step is used to construct the subproblem for the next step. We also show how the nonsmoothness can be handled efficiently by using spline approximations. The problem is then solved using a primal-dual interior-point method.

If a higher accuracy is needed, we do a crossover to an active set method. Our numerical tests show that we can solve large scale problems efficiently and accurately.
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Lehmann, Sonja [Verfasser], and Klaus [Akademischer Betreuer] Schittkowski. "A strictly feasible sequential convex programming method / Sonja Lehmann. Betreuer: Klaus Schittkowski." Bayreuth : Universitätsbibliothek Bayreuth, 2011. http://d-nb.info/1018017712/34.

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Li, Xinxin. "Some operator splitting methods for convex optimization." HKBU Institutional Repository, 2014. https://repository.hkbu.edu.hk/etd_oa/43.

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Many applications arising in various areas can be well modeled as convex optimization models with separable objective functions and linear coupling constraints. Such areas include signal processing, image processing, statistical learning, wireless networks, etc. If these well-structured convex models are treated as generic models and their separable structures are ignored in algorithmic design, then it is hard to effectively exploit the favorable properties that the objective functions possibly have. Therefore, some operator splitting methods have regained much attention from different areas for solving convex optimization models with separable structures in different contexts. In this thesis, some new operator splitting methods are proposed for convex optimiza- tion models with separable structures. We first propose combining the alternating direction method of multiplier with the logarithmic-quadratic proximal regulariza- tion for a separable monotone variational inequality with positive orthant constraints and propose a new operator splitting method. Then, we propose a proximal version of the strictly contractive Peaceman-Rachford splitting method, which was recently proposed for the convex minimization model with linear constraints and an objective function in form of the sum of two functions without coupled variables. After that, an operator splitting method suitable for parallel computation is proposed for a convex model whose objective function is the sum of three functions. For the new algorithms, we establish their convergence and estimate their convergence rates measured by the iteration complexity. We also apply the new algorithms to solve some applications arising in the image processing area; and report some preliminary numerical results. Last, we will discuss a particular video processing application and propose a series of new models for background extraction in different scenarios; to which some of the new methods are applicable. Keywords: Convex optimization, Operator splitting method, Alternating direction method of multipliers, Peaceman-Rachford splitting method, Image processing
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Theußl, Stefan, Florian Schwendinger, and Kurt Hornik. "ROI: An extensible R Optimization Infrastructure." WU Vienna University of Economics and Business, 2019. http://epub.wu.ac.at/5858/1/ROI_StatReport.pdf.

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Optimization plays an important role in many methods routinely used in statistics, machine learning and data science. Often, implementations of these methods rely on highly specialized optimization algorithms, designed to be only applicable within a specific application. However, in many instances recent advances, in particular in the field of convex optimization, make it possible to conveniently and straightforwardly use modern solvers instead with the advantage of enabling broader usage scenarios and thus promoting reusability. This paper introduces the R Optimization Infrastructure which provides an extensible infrastructure to model linear, quadratic, conic and general nonlinear optimization problems in a consistent way. Furthermore, the infrastructure administers many different solvers, reformulations, problem collections and functions to read and write optimization problems in various formats.
Series: Research Report Series / Department of Statistics and Mathematics
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Wright, Stephen E. "Convergence and approximation for primal-dual methods in large-scale optimization /." Thesis, Connect to this title online; UW restricted, 1990. http://hdl.handle.net/1773/5751.

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Books on the topic "Programming (Mathematics) Convex programming"

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Neil, Cameron. Introduction to linear and convex programming. Cambridge: Cambridge University Press, 1985.

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Șandru, Ovidiu-Ilie. Noneuclidean convexity: Applications in the programming theory. București: Editura Tehnică, 1998.

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Hiriart-Urruty, Jean-Baptiste. Fundamentals of convex analysis. Berlin: Springer, 2001.

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1944-, Lemaréchal Claude, ed. Fundamentals of convex analysis. Berlin: Springer, 2001.

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

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Foundations of optimization. New York: Springer, 2010.

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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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Convex analysis and global optimization. Dordrecht: Kluwer Academic Publishers, 1998.

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Hiriart-Urruty, Jean-Baptiste. Convex analysis and minimization algorithms. 2nd ed. Berlin: Springer-Verlag, 1996.

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Hiriart-Urruty, Jean-Baptiste. Convex analysis and minimization algorithms. Berlin: Springer-Verlag, 1993.

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Book chapters on the topic "Programming (Mathematics) Convex programming"

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Barbu, Viorel, and Teodor Precupanu. "Convex Programming." In Springer Monographs in Mathematics, 153–232. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-2247-7_3.

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Peressini, Anthony L., J. J. Uhl, and Francis E. Sullivan. "Convex Sets and Convex Functions." In The Mathematics of Nonlinear Programming, 37–81. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-1025-2_2.

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Borwein, Jonathan M., and D. Russell Luke. "Duality and Convex Programming." In Handbook of Mathematical Methods in Imaging, 1–44. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-3-642-27795-5_7-4.

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Borwein, Jonathan M., and D. Russell Luke. "Duality and Convex Programming." In Handbook of Mathematical Methods in Imaging, 229–70. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-0-387-92920-0_7.

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Borwein, Jonathan M., and D. Russell Luke. "Duality and Convex Programming." In Handbook of Mathematical Methods in Imaging, 257–304. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-0790-8_7.

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Schittkowski, K., and C. Zillober. "Sequential Convex Programming Methods." In Lecture Notes in Economics and Mathematical Systems, 123–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-88272-2_8.

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Auslender, Alfred. "Numerical methods for nondifferentiable convex optimization." In Mathematical Programming Studies, 102–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0121157.

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Peressini, Anthony L., J. J. Uhl, and Francis E. Sullivan. "Convex Programming and the Karush-Kuhn-Tucker Conditions." In The Mathematics of Nonlinear Programming, 156–214. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-1025-2_5.

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Ponstein, J. "From Convex to Mixed Programming." In Lecture Notes in Economics and Mathematical Systems, 71–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-45610-7_4.

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Courtillot, M. "A METHOD FOR CONVEX PROGRAMMING." In Proceedings of the Princeton Symposium on Mathematical Programming, 594. Princeton: Princeton University Press, 2015. http://dx.doi.org/10.1515/9781400869930-042.

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Conference papers on the topic "Programming (Mathematics) Convex programming"

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Jiang, Tao, and Mehran Chirehdast. "A Systems Approach to Structural Topology Optimization: Designing Optimal Connections." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/dac-1474.

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Abstract In this paper, structural topology optimization is extended to systems design. Locations and patterns of connections in a structural system that consists of multiple components strongly affect its performance. Topology of connections is defined, and a new classification for structural optimization is introduced that includes the topology optimization problem for connections. A mathematical programming problem is formulated that addresses this design problem. A convex approximation method using analytical gradients is used to solve the optimization problem. This solution method is readily applicable to large-scale problems. The design problem presented and solved here has a wide range of applications in all areas of structural design. The examples provided here are for spot-weld and adhesive bond joints. Numerous other potential applications are suggested.
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Shen, Xinyue, Steven Diamond, Yuantao Gu, and Stephen Boyd. "Disciplined convex-concave programming." In 2016 IEEE 55th Conference on Decision and Control (CDC). IEEE, 2016. http://dx.doi.org/10.1109/cdc.2016.7798400.

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Shen, Xinyue, Steven Diamond, Madeleine Udell, Yuantao Gu, and Stephen Boyd. "Disciplined multi-convex programming." In 2017 29th Chinese Control And Decision Conference (CCDC). IEEE, 2017. http://dx.doi.org/10.1109/ccdc.2017.7978647.

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Shi, Yingying, Zhihui Li, and Jiannan Wang. "E-convex Bilevel Programming." In Its Applications and Embedded Sys (CDEE). IEEE, 2010. http://dx.doi.org/10.1109/cdee.2010.17.

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Hsu, Justin, Zhiyi Huang, Aaron Roth, and Zhiwei Steven Wu. "Jointly Private Convex Programming." In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2015. http://dx.doi.org/10.1137/1.9781611974331.ch43.

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Pacheco, Ana, Anabela Gomes, Joana Henriques, Ana Maria de Almeida, and António José Mendes. "Mathematics and programming." In the 9th International Conference. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1500879.1500963.

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Luo, Xiaomei, K. Wong, Yiqiang Wu, and Chisheng Li. "Optimal Transceiver Design via Convex Programming." In 2006 8th international Conference on Signal Processing. IEEE, 2006. http://dx.doi.org/10.1109/icosp.2006.344532.

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Rivera, Mariano, Oscar Dalmau, and Josue Tago. "Image segmentation by convex quadratic programming." In 2008 19th International Conference on Pattern Recognition (ICPR). IEEE, 2008. http://dx.doi.org/10.1109/icpr.2008.4761385.

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Peng Du, Shih-Hung Weng, Xiang Hu, and Chung-Kuan Cheng. "Power grid sizing via convex programming." In 2011 IEEE 9th International Conference on ASIC (ASICON 2011). IEEE, 2011. http://dx.doi.org/10.1109/asicon.2011.6157190.

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Xiong, Dapeng, Guoxiang Gu, and Kemin Zhou. "Identification in hH∞ via convex programming." In 1993 American Control Conference. IEEE, 1993. http://dx.doi.org/10.23919/acc.1993.4793129.

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Reports on the topic "Programming (Mathematics) Convex programming"

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Jarre, Florian. Interior-Point Methods for Convex Programming. Fort Belvoir, VA: Defense Technical Information Center, November 1990. http://dx.doi.org/10.21236/ada231372.

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McCormick, Garth P., and Christoph Witzgall. On weakly analytic and faithfully convex functions in convex programming. Gaithersburg, MD: National Institute of Standards and Technology, 2000. http://dx.doi.org/10.6028/nist.ir.6426.

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McCormick, Garth P. Limits of SUMT trajectories in convex programming. Gaithersburg, MD: National Institute of Standards and Technology, 1997. http://dx.doi.org/10.6028/nist.ir.6074.

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Jarre, Florian, and Michael A. Saunders. Practical Aspects of an Interior-Point Method for Convex Programming. Fort Belvoir, VA: Defense Technical Information Center, July 1991. http://dx.doi.org/10.21236/ada239457.

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