On Minimax Fractional Optimality Conditions with Invexity

AbstractUnder different forms of invexity conditions, sufficient Kuhn–Tucker conditions and three dual models are presented for the minimax fractional programming

On Nonsmooth Semi-Infinite Minimax Programming Problem with (

We are interested in a nonsmooth minimax programming Problem (SIP). Firstly, we establish the necessary optimality conditions theorems for Problem (SIP) when using the well-known Caratheodory's theorem. Under the Lipschitz (Φ,ρ)-invexity assumptions, we derive the sufficiency of the necessary optimality conditions for the same problem. We also formulate dual and establish weak, strong, and strict converse duality theorems for Problem (SIP) and its dual. These results extend several known results to a wider class of problems

Security-constrained dispatch with controllable loads for integrating stochastic wind energy

This paper presents a bi-level consumer-utility optimization model to schedule an energy consumption pattern of controllable loads in the face of a time varying price function depending on system conditions and market operations. The controllable loads are classified into three types based on their natures and operating characteristics for an upper-level consumer's problem. To formulate the stochastic wind generators, a security-constrained optimal power flow (SCOPF) model is proposed for a lower-level utility's problem to consider various wind power scenarios. We then convert the bi-level model into a single-level of mathematical program with equilibrium constraints' (MPECs) problem to obtain the optimal load scheduling results. Finally, a simple case study is conducted to demonstrate the feasibility of the method. © 2012 IEEE.published_or_final_versio

Order generalised gradient and operator inequalities

We introduce the notion of order generalised gradient, a generalisation of the notion of subgradient, in the context of operator-valued functions. We state some operator inequalities of Hermite-Hadamard and Jensen types. We discuss the connection between the notion of order generalised gradient and the Gâteaux derivative of operator-valued functions. We state a characterisation of operator convexity via an inequality concerning the order generalised gradient

On Nonsmooth Semi-Infinite Minimax Programming Problem with (Φ, )-Invexity

We are interested in a nonsmooth minimax programming Problem (SIP). Firstly, we establish the necessary optimality conditions theorems for Problem (SIP) when using the well-known Caratheodory's theorem. Under the Lipschitz (Φ, )-invexity assumptions, we derive the sufficiency of the necessary optimality conditions for the same problem. We also formulate dual and establish weak, strong, and strict converse duality theorems for Problem (SIP) and its dual. These results extend several known results to a wider class of problems

Duality in Minimax Fractional Programming Problem Involving Nonsmooth Generalized (F, α, ρ, d)-Convexity

Abstract: In this paper, we discuss nondifferentiable minimax fractional programming problem where the involved functions are locally Lipschitz. Furthermore, weak, strong and strict converse duality theorems are proved in the setting of Mond-Weir type dual under the assumption of generalized (F, α, ρ, d)-convexity