Altannar Chinchuluun

Pareto Optimality, Game Theory and Equilibria

Part I Game and Game Theory.- Minimax: Existence and Stability.- Recent Advances in Minimax Theory and Applications.- On Noncooperative Games, Minimax Theorems and Equilibrium Problems.- Nonlinear Games.- Scalar Asymptotic Contractivity and Fixed-Points for Nonexpansive Mappings on Unbounded Sets.- Cooperative Combinatorial Games.- Algorithmic Cooperative Game Theory.- A Survey of Bicooperative Game Theory.- Cost Allocation in Combinatorial Optimization Games.- Time-Dependent Equilibrium Problems.- Differential Games of Multiple Agents and Geometrical Structures.- Convexity in Differential Games.- Game Dynamic Problems for Systems with Fractional Derivatives.- Projected Dynamical Systems, Evolutionary Variational Inequalities, Applications, and a Computational Procedure.- Strategic Audit Policies Without Commitment.- Optimality and Efficiency in Auctions Design: A Survey.- Part II Multiobjective, KKT, Bilevel.- Solution Concepts and an Approximation Kuhn-Tucker Approach for Fuzzy Multi-Objective Linear Bilevel Programming.- Pareto Optimality.- Multiobjective Optimization: A Brief Overview.- Parametric Multiobjective Optimization.- Part III Applications.- The Extended Linear Complementarity Problem and Its Applications in Analysis and Control of Discrete-Event Systems.- Traffic Assignmetn: Equilibrium Models.- Investment Paradoxes in Electricity Networks.- Algorithms for Network Interdiction and Fortification Games.- Game Theoretical Approaches in Wireless Networks.- A Military Application of Viability: Winning Cones, Differential Inclusions and Lanchester Type Models for Combat.- Statics and Dynamics of Global Supply Chain Networks.- Game Theory Models and Their Applications in Inventory Management in Supply Chain.

A survey of recent developments in multiobjective optimization

Abstract 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

Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity

\mathcal{NP}

Multilevel (Hierarchical) Optimization: Complexity Issues, Optimality Conditions, Algorithms

-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.

Optimality Conditions and Duality for Multiobjective Programming Involving (C, α, ρ, d) type-I Functions

Abstract 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.

Theoretical and algorithmic advances in multi-parametric programming and control

In this chapter we discuss some algorithmic and theoretical results on multilevel programming including complexity issues, optimality conditions, and algorithmic methods for solving multilevel programming problems. We also discuss an approach, which is called the multivariate partition approach, for solving a single-level mathematical programming problem based on its equivalent multilevel programming formulation.

Game Theory Models and Their Applications in Inventory Management and Supply Chain

In this chapter, we present a unified formulation of generalized convex functions. Based on these concepts, sufficient optimality conditions for a nondifferentiable multiobjective programming problem are presented. We also introduce a general Mond-Weir type dual problem of the problem and establish weak duality theorem under generalized convexity assumptions. Strong duality result is derived using a constraint qualification for nondifferentiable multiobjective programming problems.

Multiobjective Programming Problems Under Generalized Convexity

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.

Optimization in Wireless Networks

Analysis of supply chain politics can benefit from applying game-theory concepts extensively. Game theory tries to enlighten the interactions between individuals or groups of people whose goals are ...

Optimization, Simulation, and Control

In this chapter, we consider optimality conditions and duality for some multiobjective programming problems with generalized convexity. In particularly, the general multiobjective programming, multiobjective fractional programming and multiobjective variational programming will be discussed.