Multiobjective Optimization (MO) has many applications in such fields as the Internet, finance, biomedicine, management science, game theory and engineering. However, solving MO problems is not an easy task. Searching for all Pareto optimal solutions is expensive and a time consuming process because there are usually exponentially large (or infinite) Pareto optimal solutions. Even for simple problems determining whether a point belongs to the Pareto set is N P-hard. In this paper, we discuss recent developments in MO. These include optimality conditions, applications, global optimization techniques, the new concept of epsilon Pareto optimal solution, and heuristics.

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This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system.

In this paper, we consider nondifferentiable multiobjective fractional programming problems. A concept of generalized convexity, which is called (C, α, ρ, d)-convexity, is first discussed. Based on this generalized convexity, we obtain efficiency conditions for multiobjective fractional programming (MFP). Furthermore, we establish duality results for three types of dual problems of (MFP) and present the corresponding duality theorems.Keywords Multiobjective fractional programming problem · (C, α, ρ, d)-convexity · Efficiency conditions · Global efficient solution · Duality Several authors have been interested in generalization of convexity in connection with sufficiency and duality theorems in optimization problems (Hiriart-Urruty 1978;Kaul and Kaur 1985). It is possible to generalize the notion of convexity and extend the validity of theorems to larger classes of optimization problems. Therefore, several classes of generalized convex functions are introduced by researchers including Schmitendorf introduced a new class of generalized type I vector-valued functions, which are generalizations of type I function introduced by Hanson and Mond (1987), and proved duality theorems for differentiable multiobjective optimization problems A. Chinchuluun · P.M. Pardalos ( )