Results 151 to 160 of about 136,528 (194)

Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization. [PDF]

Philos Trans A Math Phys Eng Sci
Burger M, Kabri S, Korolev Y, Roith T, Weigand L.   +4 more
europepmc   +1 more source

NONDIFFERENTIABLE SECOND-ORDER SYMMETRIC DUALITY [PDF]

Asia-Pacific Journal of Operational Research, 2005
A pair of Mond–Weir type nondifferentiable second-order symmetric primal and dual problems in mathematical programming is formulated. Weak duality, strong duality, and converse duality theorems are established under η-pseudobonvexity assumptions. Symmetric minimax mixed integer primal and dual problems are also investigated. Moreover, the self duality
I. AHMAD, Z. HUSAIN
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Symmetric Duality via Conjugate Duality

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1977
AbstractSymmetric pairs of programming problems involving square roots of quadratic forms have been studied by a number of authors. By applying the methods of conjugate duality theory to generalizations of these problems we readily obtain extensions of most known results guaranteeing duality of this pair.
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On Symmetric Duality in Nonlinear Programming

Operations Research, 1973
In this study we generalize the formulation of symmetric duality introduced by Dantzig, Eisenberg, and Cottle to include the case where the constraints of the inequality type are defined via closed convex cones and their polars. The new formulation retains the symmetric properties of the original programs.
Bazaraa, M. S., Goode, J. J.
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Symmetrical duality vertex

Il Nuovo Cimento A, 1970
A symmetrical formula for the on-mass-shell three-particle vertex of the generalized Veneziano model is derived. No attempt is made to isolate the contributions corresponding to the different angularmomentum components of the three particles.
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Multiobjective symmetric duality involving cones

European Journal of Operational Research, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Suneja, S. K., Aggarwal, Sunila, Davar, Sonia   +2 more
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Symmetric Duality for Continuous Linear Programs

SIAM Journal on Applied Mathematics, 1970
A strong duality theorem for continuous linear programs is established and a two-level maximal principle derived as a consequence. The method of proof is constructive, indicating that optimal solutions of approximating linear programs converge to the optimal solution of the continuous problem.
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On Mixed Symmetric Duality in Mathematical Programming

OPSEARCH, 1999
A new symmetric dual formulation, called the mixed symmetric dual, is presented for a class of nonlinear programming problems and various duality theorems are established. This mixed formulation unifies the two existing and well known symmetric dual formulations in the literature.
Chandra, S., Husain, I., Abha
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Secound Order Symmetric Duality with Generalized Convexity

OPSEARCH, 2001
Two distinct pairs of secound order symmetric dual programs are considered and appropriate duality theorems are established under η1-convexity/η1-concavity and η1-pseudoconvexity η2-psecoudoconcavity of the kernel function K(x,y). Assuming the additional hypothesis of skew symmetry for K(x,y) these programs are shown to be self dual.
Gulati, T. R., Ahmad, Izhar, Husain, I.
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