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In the present paper, a newly combined higher-order non-differentiable symmetric duality in scalar-objective programming over arbitrary cones is formulated. In literature we have discussed primal-dual results with arbitrary cones, while in this article, we have derived combined result with one model over arbitrary cones. The theorems of duality are derived for these problems under η-pseudoinvexity/η-invexity/C-pseudoconvexity/C-convexity speculations over arbitrary cones.

The present work frames a pair of symmetric dual problems for second order nondifferentiable fractional variational problems over cone constraints with the help of support functions. Weak, strong and converse duality theorems are derived under second order F-convexity assumptions. By removing time dependency, static case of the problem is obtained. Suitable numerical example is constructed. [ABSTRACT FROM AUTHOR]

A pair of mixed non-differentiable second-order symmetric dual programmesover cones is considered. Weak, strong and converse duality theorems are establishedunder second-order (F, ) convexity/pseudo-convexity assumptions. Special cases arealso discussed to show that this paper extends some known results in the literature.

We consider the problem of optimally covering solid bodies by a given number of spheres. The mathematical modelling of this problem leads to a min–max–min formulation which, in addition to its intrinsic multi-level nature, has the significant characteristic of being non-differentiable. The use of the hyperbolic smoothing technique engenders a simple one-level nonlinear programming problem and allows overcoming the main difficulties presented by the original one. To illustrate the performance of the method we present computational results for two large test covering problems with up to 1,200,000 voxels. The first problem is the covering of a ring torus whose optimal solution is known whenever the number of covering spheres is small, and the second problem is a generic test problem. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the optimization techniques for solving a class of non-differentiable optimization problems are investigated. The non-differentiable programming is transformed into an equivalent or approximating differentiable programming. Based on Karush–Kuhn–Tucker optimality conditions and projection method, a neural network model is constructed. The proposed neural network is proved to be globally stable in the sense of Lyapunov and can obtain an exact or approximating optimal solution of the original optimization problem. An example shows the effectiveness of the proposed optimization techniques. [Copyright &y& Elsevier]

Theoretical aspects of the programming problem of maximizing the minimum value of a set of linear functionals subject to linear constraints are explored. Solution strategies are discussed and an optimality condition is developed. An algorithm is also presented. [ABSTRACT FROM AUTHOR]