scholarly journals The Convexity Assumption: Infants use Knowledge of Objects to Interpret Static Monocular Information by 5 Months

2010 ◽  
Vol 10 (7) ◽  
pp. 497-497
Author(s):  
S. Corrow ◽  
A. Yonas ◽  
C. Granrud
Keyword(s):  
Convexity Assumption

Optimality of Approximate Quasi-Weakly Efficient Solutions for Vector Equilibrium Problems via Convexificators

2021 ◽  
Author(s):  
Guolin Yu ◽  
Siqi Li ◽  
Xiao Pan ◽  
Wenyan Han
Keyword(s):  
Optimality Condition ◽  
Generalized Convexity ◽  
Equilibrium Problems ◽  
Efficient Solutions ◽  
Sufficient Optimality Condition ◽  
Necessary Optimality Condition ◽  
Weakly Efficient Solutions ◽  
Convexity Assumption ◽  
Pseudoconvex Function ◽  
Vector Equilibrium

This paper is devoted to the investigation of optimality conditions for approximate quasi-weakly efficient solutions to a class of nonsmooth Vector Equilibrium Problem (VEP) via convexificators. First, a necessary optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is presented by making use of the properties of convexificators. Second, the notion of approximate pseudoconvex function in the form of convexificators is introduced, and its existence is verified by a concrete example. Under the introduced generalized convexity assumption, a sufficient optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is also established. Finally, a scalar characterization for approximate quasi-weakly efficient solutions to problem (VEP) is obtained by taking advantage of Tammer’s function.

scholarly journals ON EQUALITY CONDITION FOR TRACE JENSEN INEQUALITY IN SEMI-FINITE VON NEUMANN ALGEBRAS

2008 ◽  
Vol 19 (04) ◽  
pp. 481-501 ◽  
Author(s):  
TETSUO HARADA ◽  
HIDEKI KOSAKI
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Adjoint Operator ◽  
Strict Convexity ◽  
Jensen Inequality ◽  
Von Neumann ◽  
Convexity Assumption ◽  
Finite Von Neumann Algebra ◽  
Equality Condition ◽  
Finite Von Neumann Algebras

Let τ be a faithful semi-finite normal trace on a semi-finite von Neumann algebra, and f(t) be a convex function with f(0) = 0. The trace Jensen inequality states τ(f(a* xa)) ≤ τ(a* f(x)a) for a contraction a and a self-adjoint operator x. Under certain strict convexity assumption on f(t), we will study when this inequality reduces to the equality.

scholarly journals A nonmonotone modified BFGS algorithm for nonconvex unconstrained optimization problems

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1283-1296
Author(s):  
Keyvan Amini ◽  
Somayeh Bahrami ◽  
Shadi Amiri
Keyword(s):  
Unconstrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Hessian Matrix ◽  
Convergence Properties ◽  
Convexity Assumption ◽  
Unconstrained Optimization Problems ◽  
Secant Condition ◽  
Approximate Hessian ◽  
Modified Secant Condition

In this paper, a modified BFGS algorithm is proposed to solve unconstrained optimization problems. First, based on a modified secant condition, an update formula is recommended to approximate Hessian matrix. Then thanks to the remarkable nonmonotone line search properties, an appropriate nonmonotone idea is employed. Under some mild conditions, the global convergence properties of the algorithm are established without convexity assumption on the objective function. Preliminary numerical experiments are also reported which indicate the promising behavior of the new algorithm.

scholarly journals On the honeycomb conjecture for Robin Laplacian eigenvalues

2019 ◽  
Vol 21 (02) ◽  
pp. 1850007 ◽  
Author(s):  
Dorin Bucur ◽  
Ilaria Fragalà
Keyword(s):  
Torsional Rigidity ◽  
Cluster Problem ◽  
Laplacian Eigenvalues ◽  
Convexity Assumption ◽  
Robin Laplacian ◽  
Cheeger Sets ◽  
Optimal Cluster

We prove that the optimal cluster problem for the sum/the max of the first Robin eigenvalue of the Laplacian, in the limit of a large number of convex cells, is asymptotically solved by (the Cheeger sets of) the honeycomb of regular hexagons. The same result is established for the Robin torsional rigidity. In the specific case of the max of the first Robin eigenvalue, we are able to remove the convexity assumption on the cells.

scholarly journals Nekhoroshev-Stability ofL4andL5in the Spatial Restricted Problem

1999 ◽  
Vol 172 ◽  
pp. 445-446 ◽  
Author(s):  
Giancarlo Benettin ◽  
Francesco Fassò ◽  
Massimiliano Guzzo
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Critical Mass ◽  
Kam Theory ◽  
Birkhoff Normal Form ◽  
Three Body Problem ◽  
Arnold Diffusion ◽  
Convexity Assumption ◽  
Three Body ◽  
Nekhoroshev Stability

The Lagrangian equilateral pointsL4andL5of the restricted circular three-body problem are elliptic for all values of the reduced massμbelow Routh’s critical massμR≈ .0385. In the spatial case, because of the possibility of Arnold diffusion, KAM theory does not provide Lyapunov-stability. Nevertheless, one can consider the so-called ‘Nekhoroshev-stability’: denoting byda convenient distance from the equilibrium point, one asks whetherfor any small єe > 0, with positiveaandb. Until recently this problem, as more generally the problem of Nekhoroshev-stability of elliptic equilibria of Hamiltonian systems, was studied only under some arithmetic conditions on the frequencies, and thus onμ(see e.g .Giorgilli, 1989). Our aim was instead considering all values ofμup toμR. As a matter of fact, Nekhoroshev-stability of elliptic equilibria, without any arithmetic assumption on the frequencies, was proved recently under the hypothesis that the fourth order Birkhoff normal form of the Hamiltonian exists and satisfies a ‘quasi-convexity’ assumption (Fassòet al, 1998; Guzzoet al, 1998; Niedermann, 1998).

A Nonmonotone Modified BFGS Method for Non-Convex Minimization

2014 ◽  
Vol 556-562 ◽  
pp. 4023-4026
Author(s):  
Ting Feng Li ◽  
Zhi Yuan Liu ◽  
Sheng Hui Yan
Keyword(s):  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Convergence Property ◽  
Bfgs Method ◽  
Remarkable Feature ◽  
Convexity Assumption ◽  
Unconstrained Optimization Problems ◽  
Global Convergence Property ◽  
Large Scale Unconstrained Optimization

In this paper, a modification BFGS method with nonmonotone line-search for solving large-scale unconstrained optimization problems is proposed. A remarkable feature of the proposed method is that it possesses a global convergence property even without convexity assumption on the objective function. Some numerical results are reported which illustrate that the proposed method is efficient

scholarly journals Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

2015 ◽  
Vol 145 (1) ◽  
pp. 31-45 ◽  
Author(s):  
Barbara Brandolini ◽  
Francesco Chiacchio ◽  
Cristina Trombetti
Keyword(s):  
Neumann Problems ◽  
Convexity Assumption ◽  
Planar Domains ◽  
Isoperimetric Constant ◽  
Linear And Nonlinear ◽  
Neumann Eigenvalue ◽  
The One ◽  
Nonlinear Neumann Problems ◽  
Sharp Lower Bound ◽  
Better Than

In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p > 1) in a Lipschitz bounded domain Ω in ℝn. Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω. In a suitable class of convex planar domains, our bound turns out to be better than the one provided by the Payne—Weinberger inequality.

scholarly journals Evidence for a general convexity assumption in 6-month-old infants.

2013 ◽  
Vol 13 (9) ◽  
pp. 736-736
Author(s):  
J. Mathison ◽  
S. Corrow ◽  
V. Adamson ◽  
C. Granrud ◽  
A. Yonas
Keyword(s):  
Convexity Assumption ◽  
General Convexity

scholarly journals Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming

2020 ◽  
Author(s):  
Mohsine Jennane ◽  
El Mostafa Kalmoun ◽  
Lahoussine Lafhim
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Convexity Assumption ◽  
Locally Lipschitz ◽  
Infinite Programming ◽  
Asymptotic Convexity ◽  
Interval Valued

We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraints functions need not to be locally Lipschitz. Using Abadie's constraint qualification and convexificators, we provide  Karush-Kuhn-Tucker necessary optimality conditions by converting the initial problem into a bi-criteria optimization problem. Furthermore, we establish sufficient optimality conditions  under the asymptotic convexity assumption.

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