In this paper, we introduce the notion of a second-order coneconvex function involving second-order directional derivative. Also, second-order cone-pseudoconvex, second-order cone-quasiconvex and other related functions are defined. Second-order optimality and Mond-Weir type duality results are derived for a vector optimization problem over cones using the introduced classes of functions.

A multiobjective nonlinear programming problem is considered. Sufficiency theorems are derived for efficient and properly efficient solutions under generalized (F, ρ)-convexity assumptions. Weak, strong and strict converse duality theorems are established for a general Mond–Weir type dual relating properly efficient solutions of the primal and dual problems.

Considering a general optimization problem, we attach to it by means of perturbation theory two dual problems having in the constraints a subdifferential inclusion relation. When the primal problem and the perturbation function are particularized different new dual problems are obtained. In the special case of a constrained optimization problem, the classical Wolfe and Mond–Weir duals, respecti...

Lord Weir, Sir James Lithgow and Andrew Rae Duncan were three close friends who grew up within a few miles of each other in Victorian Glasgow, went on to have uncommonly successful care...

Abstract In this research, the models of Inflatable weirs with internal pressures 0.5 and 1.4 at three heights 0.15, 0.2 0.25 m were constructed. The deflectors used in two geometric sections, including rectangular triangular shapes, they installed angles 30, 45, 60 degrees downstream weir body. results showed that value Cd changes between 0.28 0.35 while range ratio upstream flow head on crest...

Local scouring in the downstream of hydraulic structures is one of the important issues in river and hydraulic engineering, which involves a lot of costs every year, so the prediction of the rate of scour is important in hydraulic design. Side weirs are the most important of hydraulic structures that are used in passing flow. This study investigate the scouring due to falling jet from side weir...