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Relevant bibliographies by topics / Concave and convex functions

Academic literature on the topic 'Concave and convex functions'

Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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Journal articles on the topic "Concave and convex functions"

1

Borwein, David, and Julien Grivaux. "Convex and Concave Functions: 11009." American Mathematical Monthly 112, no. 1 (January 1, 2005): 92. http://dx.doi.org/10.2307/30037402.

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Meyer, M., G. Mokobodzki, and M. Rogalski. "Convex bodies and concave functions." Proceedings of the American Mathematical Society 123, no. 2 (February 1, 1995): 477. http://dx.doi.org/10.1090/s0002-9939-1995-1254848-2.

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Lynch, James D. "When Is a Renewal Process Convexly Parameterized in Its Mean Parameterization?" Probability in the Engineering and Informational Sciences 11, no. 1 (January 1997): 43–48. http://dx.doi.org/10.1017/s0269964800004666.

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The convex (concave) parameterization of a generalized renewal process is considered in this paper. It is shown that if the interrenewal times have log concave distributions or have log concave survival functions (i.e., an increasing failure rate distribution), then the renewal process is convexly (concavely) parameterized in its mean parameterization.

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Meyer, Clifford A., and Christodoulos A. Floudas. "Convex envelopes for edge-concave functions." Mathematical Programming 103, no. 2 (April 28, 2005): 207–24. http://dx.doi.org/10.1007/s10107-005-0580-9.

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Nemirovski, Arkadi. "On self-concordant convex–concave functions." Optimization Methods and Software 11, no. 1-4 (January 1999): 303–84. http://dx.doi.org/10.1080/10556789908805755.

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Moudafi, Abdellatif. "Well-behaved asymptotical convex-concave functions." Numerical Functional Analysis and Optimization 18, no. 9-10 (January 1997): 1013–21. http://dx.doi.org/10.1080/01630569708816806.

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Nikodem, Kazimierz. "Midpoint convex functions majorized by midpoint concave functions." Aequationes Mathematicae 31, no. 1 (December 1986): 322. http://dx.doi.org/10.1007/bf02188199.

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Nikodem, Kazimierz. "Midpoint convex functions majorized by midpoint concave functions." Aequationes Mathematicae 32, no. 1 (December 1987): 45–51. http://dx.doi.org/10.1007/bf02311298.

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Mateljevic, Miodrag, and Miloljub Albijanic. "Lagrange’s theorem, convex functions and Gauss map." Filomat 31, no. 2 (2017): 321–34. http://dx.doi.org/10.2298/fil1702321m.

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As one of the main results we prove that if f has Lagrange unique property then f is strictly convex or concave (we do not assume continuity of the derivative), Theorem 2.1. We give two different proofs of Theorem 2.1 (one mainly using Lagrange theorem and the other using Darboux theorem). In addition, we give a few characterizations of strictly convex curves, in Theorem 3.5. As an application of it, we give characterization of strictly convex planar curves, which have only tangents at every point, by injective of the Gauss map. Also without the differentiability hypothesis we get the characterization of strictly convex or concave functions by two points property, Theorem 4.2.

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SEGAL, ALEXANDER, and BOAZ A. SLOMKA. "PROJECTIONS OF LOG-CONCAVE FUNCTIONS." Communications in Contemporary Mathematics 14, no. 05 (August 29, 2012): 1250036. http://dx.doi.org/10.1142/s0219199712500368.

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Recently, it has been proven in [V. Milman, A. Segal and B. Slomka, A characterization of duality through section/projection correspondence in the finite dimensional setting, J. Funct. Anal. 261(11) (2011) 3366–3389] that the well-known duality mapping on the class of closed convex sets in ℝn containing the origin is the only operation, up to obvious linear modifications, that interchanges linear sections with projections. In this paper, we extend this result to the class of geometric log-concave functions (attaining 1 at the origin). As the notions of polarity and the support function were recently uniquely extended to this class by Artstein-Avidan and Milman, a natural notion of projection arises. This notion of projection is justified by our result. As a consequence of our main result, we prove that, on the class of lower semi continuous non-negative convex functions attaining 0 at the origin, the polarity operation is the only operation interchanging addition with geometric inf-convolution and the support function is the only operation interchanging addition with inf-convolution.

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Dissertations / Theses on the topic "Concave and convex functions"

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Ghadiri, Hamid Reza. "Convex Functions." Thesis, Karlstads universitet, Fakulteten för teknik- och naturvetenskap, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-7473.

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Zagar, Susanna Maria. "Convex functions." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/986.

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Ma, Jie. "Heterogeneous nucleation on convex and concave spherical surfaces." Thesis, University of Portsmouth, 2008. http://eprints.port.ac.uk/15503/.

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Nucleation is a phenomenon of broad scientific interest and technological importance. It refers to the very early stages of the formation of a new phase, which can be solid, gaseous, and liquid, in a metastable parent phase. Most nucleation occurs heterogeneously unless the metastable parent phase from which the nuclei form is perfectly homogeneous and isolated from any catalyzing medium. This thesis project deals with heterogeneous nucleation on convex and concave spherical surfaces. In brief, the main achievements of the project are • An innovative analytical thermodynamic approach has been invented, which enabled rigorous thermodynamic formation of the energy barrier to nucleation, the critical radius and the shape factor, for nucleation on both convex and on concave surfaces. The rigorous thermodynamic analyses conducted have revealed a number of features for heterogeneous nucleation on convex and concave spherical surfaces as opposed to heterogeneous nucleation on a flat substrate surface. These are described in detail in Chapters 2 and 4. • Nucleation is the easiest on a concave spherical surface while it is the most difficult on a convex spherical surface assuming the contact angle and the critical embryo radius are the same. Nucleation on a flat substrate surface falls in between. This is determined by their shape factors. • The ratio R = 20r*, where R is the radius of the spherical substrate and r* is the critical embryo radius, (always define the symbols when they are first used. No one knows what they mean. R could be gas constant) can be regarded as a sufficiently accurate boundary that distinguishes between spherical and flat substrates for heterogeneous nucleation. • The investigation of the growth of crystal nuclei on a convex spherical surface has revealed that no growth barrier exists to the growth of a nucleus on a convex spherical substrate surface regardless of R < r* or R > r*. All nuclei formed on a convex spherical substrate surface are thus transformation nuclei. Turnbull’s transformation nucleus model or the recently developed free growth model does not apply to the growth of a spherical-cap nucleus on a convex spherical surface. • For heterogeneous nucleation in undercooled liquid metals, the cap thickness varies in a very narrow range by just a few angstroms and is typically about a few atomic layers thick according to Turnbull’s nucleation rate equation. The variations in the cap thickness are generally limited to less than 1Å when the contact angle Ɵ is varied in the range from 0° to 45°. It is anticipated that these findings will help to better understand the classical models for heterogeneous nucleation and provide new insights into the control of heterogeneous nucleation where convex or concave spherical substrate surfaces are involved.

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Choe, Byung-Tae. "Essays on concave and homothetic utility functions." Uppsala : Stockholm, Sweden : s.n. ; Distributor, Almqvist & Wiksell International, 1991. http://catalog.hathitrust.org/api/volumes/oclc/27108685.html.

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Brennan, Derek. "Convex functions, majorization properties and the convex conjugate transform." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=81603.

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Let Kw(t) := inf∥P∥ 22≤t 01 |1 - P(theta)|2w(theta) dtheta, where w ≥ 0 is a decreasing function and P ∈ L2([0,1], Leb.).
Then we have Kw ≤ Kv ↔01 1wq +l dtheta ≥ 01 1vq+l dtheta ∀ lambda ≥ 0.
We present two similar proofs of this result, which are analogous to the well-known majorization theorem: Let v, w ≥ 0 be decreasing functions, and suppose 01 w(theta)dtheta = 01 v(theta)dtheta.
Then Fw ≤ Fv ↔01 (w(theta) - x)+ dtheta ≥ 01 (v(theta) - x)+ dtheta ∀ x ≥ 0, where F w(t) = t1 w(theta)dtheta. Since our proofs of this result rely mainly on the convex conjugate transform, or Legendre transform, we include an exposition of convex functions and convex conjugate transforms.

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Caglar, Umut. "Divergence And Entropy Inequalities For Log Concave Functions." Case Western Reserve University School of Graduate Studies / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=case1400598757.

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Saysupan, Sutthilak. "Design and Fabrication of convex and concave Lenses made of Transparent Liquids." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-295596.

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This report studies about optical convex and concavelenses, made of liquid materials. Design proposals of the liquidlenses and the required supporting structure (container), as wellas manufacturing method have been investigated. 8 lenses aredesigned: 4 convex and 4 concave. The theoretical expectationsare validated by simulation and experimental results. The methodhave both advantages and disadvantages. The materials in thelenses are water, syrup, benzyl benzoate and bromone naphtha-lene.
Undersökning gällande optiska linser konvexa och konkava, bestående av flytande material. Designförslag av linser och skall, samt tillverkningsmetod har undersökts. De teoretiska förväntningarna validerades genom simulering och experimentella resultat. Metoden visas har både fördelar och nackdelar. Material i de linserna som vi har undersökt är vatten, sockerlösning, bensylbensoat och Bromonaftalen.
Kandidatexjobb i elektroteknik 2020, KTH, Stockholm

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Morales, J. M. "Structured sparsity with convex penalty functions." Thesis, University College London (University of London), 2012. http://discovery.ucl.ac.uk/1355964/.

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We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in Machine Learning, Statistics and Signal Processing. It is well known that a linear regression can benefit from knowledge that the underlying regression vector is sparse. The combinatorial problem of selecting the nonzero components of this vector can be “relaxed” by regularising the squared error with a convex penalty function like the ℓ1 norm. However, in many applications, additional conditions on the structure of the regression vector and its sparsity pattern are available. Incorporating this information into the learning method may lead to a significant decrease of the estimation error. In this thesis, we present a family of convex penalty functions, which encode prior knowledge on the structure of the vector formed by the absolute values of the regression coefficients. This family subsumes the ℓ1 norm and is flexible enough to include different models of sparsity patterns, which are of practical and theoretical importance. We establish several properties of these penalty functions and discuss some examples where they can be computed explicitly. Moreover, for solving the regularised least squares problem with these penalty functions, we present a convergent optimisation algorithm and proximal method. Both algorithms are useful numerical techniques taylored for different kinds of penalties. Extensive numerical simulations highlight the benefit of structured sparsity and the advantage offered by our approach over the Lasso method and other related methods, such as using other convex optimisation penalties or greedy methods.

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Edwards, Teresa Dawn. "The box method for minimizing strictly convex functions over convex sets." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/30690.

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Semu, Mitiku Kassa. "On minimal pairs of compact convex sets and of convex functions /." [S.l. : s.n.], 2002. http://www.gbv.de/dms/zbw/36225754X.pdf.

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Books on the topic "Concave and convex functions"

1

Avriel, M. Generalized concavity. Philadelphia: Society for Industrial and Applied Mathematics, 2010.

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Choe, Byung-Tae. Essays on concave and homothetic utility functions. Uppsala: s.n., 1991.

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3

Niculescu, Constantin P., and Lars-Erik Persson. Convex Functions and Their Applications. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78337-6.

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Niculescu, Constantin P., and Lars-Erik Persson. Convex Functions and Their Applications. New York, NY: Springer New York, 2006. http://dx.doi.org/10.1007/0-387-31077-0.

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Lieven, Vandenberghe, ed. Convex optimization. Cambridge, UK: Cambridge University Press, 2006.

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6

Convex analysis. Princeton, N.J: Princeton University Press, 1997.

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Rockafellar, Ralph Tyrell. Convex Analysis. Princeton, NJ, USA: Princeton University Press, 1997.

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Liese, Friedrich. Convex statistical distances. Leipzig: B.G. Teubner Verlagsgesellschaft, 1987.

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Choi, Suhyoung. The Convex and concave decomposition of manifolds with real projective structures. [Paris, France]: Société mathématique de France, 1999.

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Discrete convex analysis. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2004.

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Book chapters on the topic "Concave and convex functions"

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Bhunia, Asoke Kumar, Laxminarayan Sahoo, and Ali Akbar Shaikh. "Convex and Concave Functions." In Springer Optimization and Its Applications, 13–27. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-32-9967-2_2.

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Kythe, Prem K. "Concave and Convex Functions." In Elements of Concave Analysis and Applications, 63–86. Boca Raton, Florida : CRC Press, [2018]: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315202259-3.

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Kythe, Prem K. "Quasi-Convex Functions." In Elements of Concave Analysis and Applications, 179–96. Boca Raton, Florida : CRC Press, [2018]: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315202259-7.

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Panik, Michael J. "Convex and Concave Real-Valued Functions." In Mathematical Analysis and Optimization for Economists, 101–23. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003164494-8-8.

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Jerison, David. "Eigenfunctions and Harmonic Functions in Convex and Concave Domains." In Proceedings of the International Congress of Mathematicians, 1108–17. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9078-6_103.

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Kiefer, By J., and J. Wolfowitz. "Asymptotically Minimax Estimation of Concave and Convex Distribution Functions. II." In Collected Papers, 803–21. New York, NY: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4613-8505-9_49.

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Cavazzuti, E., and N. Pacchiarotti. "Compactness and Boundedness for a Class of Concave-Convex Functions." In Nonsmooth Optimization and Related Topics, 23–38. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4757-6019-4_2.

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Oettli, W. "Decomposition Schemes for Finding Saddle Points of Quasi-Convex-Concave Functions." In Quantitative Methoden in den Wirtschaftswissenschaften, 31–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-74306-1_3.

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Aze, D. "Rate of convergence for the saddle points of convex-concave functions." In Trends in Mathematical Optimization, 9–23. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9297-1_1.

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Veinott, Arthur F. "Existence and characterization of minima of concave functions on unbounded convex sets." In Mathematical Programming Essays in Honor of George B. Dantzig Part II, 88–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0121077.

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Conference papers on the topic "Concave and convex functions"

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Sulaiman, W. T. "On Integral Inequalities Concerning Convex and Concave Functions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990974.

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Sulaiman, W. T. "Hardy‐Hilbert’s Integral Inequalities for Convex and Concave Functions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990975.

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Li, Mengmou, and Tao Liu. "Distributed Robust Resource Allocation with Convex-Concave Uncertain Objective Functions." In 2018 57th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE). IEEE, 2018. http://dx.doi.org/10.23919/sice.2018.8492684.

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Xiao, Yichi, Zhe Li, Tianbao Yang, and Lijun Zhang. "SVD-free Convex-Concave Approaches for Nuclear Norm Regularization." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/436.

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Minimizing a convex function of matrices regularized by the nuclear norm arises in many applications such as collaborative filtering and multi-task learning. In this paper, we study the general setting where the convex function could be non-smooth. When the size of the data matrix, denoted by m x n, is very large, existing optimization methods are inefficient because in each iteration, they need to perform a singular value decomposition (SVD) which takes O(m^2 n) time. To reduce the computation cost, we exploit the dual characterization of the nuclear norm to introduce a convex-concave optimization problem and design a subgradient-based algorithm without performing SVD. In each iteration, the proposed algorithm only computes the largest singular vector, reducing the time complexity from O(m^2 n) to O(mn). To the best of our knowledge, this is the first SVD-free convex optimization approach for nuclear-norm regularized problems that does not rely on the smoothness assumption. Theoretical analysis shows that the proposed algorithm converges at an optimal O(1/\sqrt{T}) rate where T is the number of iterations. We also extend our algorithm to the stochastic case where only stochastic subgradients of the convex function are available and a special case that contains an additional non-smooth regularizer (e.g., L1 norm regularizer). We conduct experiments on robust low-rank matrix approximation and link prediction to demonstrate the efficiency of our algorithms.

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Holding, Thomas, and Ioannis Lestas. "On the convergence to saddle points of concave-convex functions, the gradient method and emergence of oscillations." In 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE, 2014. http://dx.doi.org/10.1109/cdc.2014.7039535.

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Pekala, Barbara, Ewa Rak, Bogdan Kwiatkowski, Adam Szczur, and Rafal Rak. "The use of concave and convex functions to optimize the feed-rate of numerically controlled machine tools." In 2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2020. http://dx.doi.org/10.1109/fuzz48607.2020.9177569.

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Cao, Daoming, and Pigong Han. "Infinitely many positive energy solutions for semilinear elliptic equations with concave and convex nonlinearity." In Proceedings of the ICM 2002 Satellite Conference on Nonlinear Functional Analysis. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704283_0006.

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Ohsaki, Hiroyuki, and Masayuki Murata. "Packet marking function of active queue management mechanism: should it be linear, concave, or convex?" In Optics East, edited by Frank Huebner and Robert D. van der Mei. SPIE, 2004. http://dx.doi.org/10.1117/12.571797.

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Pao, Y. C., P. Y. Qin, and Q. S. Yuan. "A Fast Sequential Hidden-Line Removal Algorithm." In ASME 1993 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/cie1993-0079.

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Abstract A fast hidden-line removal algorithm for single convex or concave object, and multiple objects has been developed. It is applicable to both solid objects constructed with planar faces, and with curved surfaces which are represented by meshes. The invisible lines are removed in phases and the computing time in all phases is minimized. Line edges and plane elements involved in the solid object are sorted in the order of their coordinate values. Bounding rectangular boxes are used to determine the overlaps. In place of the trigonometric functions, a simplified linear function is adopted for reducing the computing time. Illustrative examples are presented to demonstrate the practical applications of the developed algorithm.

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Wang, Guanghui, Dakuan Zhao, and Lijun Zhang. "Minimizing Adaptive Regret with One Gradient per Iteration." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/383.

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To cope with non-stationary environments, recent advances in online optimization have introduced the notion of adaptive regret, which measures the performance of an online learner against different comparators within different time intervals. Previous studies have proposed various algorithms to yield low adaptive regret under different scenarios. However, all of existing algorithms need to query the gradient of the loss function at least O(log t) times in every iteration t, which hinders their applications to broad domains, especially when the evaluation of gradients is expensive. To address this limitation, we propose a series of computationally efficient algorithms for minimizing the adaptive regret of general convex, strongly convex and exponentially concave functions respectively. The key idea is to replace each loss function with a carefully designed surrogate loss, which bounds the original loss function from below. We show that the proposed algorithms only query the gradient once per iteration, and attain the same theoretical guarantees as previous optimal algorithms. Empirical results demonstrate the efficiency and effectiveness of our methods.

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Reports on the topic "Concave and convex functions"

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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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AL-Khayyal, Fais A., Reiner Horst, and Panos M. Pardalos. Global Optimization of Concave Functions Subject to Separable Quadratic Constraints and of All-Quadratic Separable Problems. Fort Belvoir, VA: Defense Technical Information Center, April 1988. http://dx.doi.org/10.21236/ada197747.

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