Abstract: We show how to use intensively local cone approximations to obtain results in some fields of optimization theory such as optimality conditions, constraint qualifications, mean value theorems and error bound.

We study firstand second-order necessary and sufficient optimality conditions for approximate weakly, properly efficient solutions of multiobjective optimization problems. Here, tangent cone, -normal cone, cones of feasible directions, second-order tangent set, asymptotic second-order cone, and Hadamard upper lower directional derivatives are used in the characterizations. The results are first...

The main objective of this research is to improvethe design and performance of the polyurethane foam-filled thin-walled aluminum grooved circular tubes using multi-response optimization (MRO) technique. The tubes are shaped with the inner and the outer circular grooves at different positions along the axis. For this aim, several numerical simulations using ABAQUS finite element explicit code ar...

The gradostat consists of multiple chemostats interconnected by mass flows and diffusion. It has been used to model biochemical systems such as wastewater treatment networks microbial activity in soil. In this paper we maximize the production biogas a at steady state. physical decision variables are water, substrate, biomass entering each tank through interconnecting pipes. Our main technical f...

many shape and topology optimization methods have been inspired from the nature. in this paper, two different optimization algorithms based on the adaptive biological growth (abg) have been applied to some structural elements. the first algorithm is developed for the shape optimization and is applied to a plate with a central hole as well as a fillet plate. the second algorithm is the soft kill...

PURPOSE To calculate the output factor (OPF) of any irregularly shaped electron beam at extended SSD. METHODS Circular cutouts were prepared from 2.0 cm diameter to the maximum possible size for 15 × 15 applicator cone. In addition, two irregular cutouts were prepared. For each cutout, percentage depth dose (PDD) at the standard SSD and doses at different SSD values were measured using 6, 9, ...

The purpose of this survey article is to introduce the reader to a very elegant formulation of convex optimization problems called conic optimization and outline its many advantages. After a brief introduction to convex optimization, the notion of convex cone is introduced, which leads to the conic formulation of convex optimization problems. This formulation features a very symmetric dual prob...