Quasi-Variational Inequality Problems over Product Sets with Quasi-monotone Operators

Quasi-variational inequalities are variational inequalities in which the constraint map depends on the current point. Due to this characteristic, specific proofs have been built to prove adapted existence results. Semicontinuity and generalized monotonicity are assumed and many efforts have been made in the last decades to use the weakest concepts. In the case of quasi-variational inequalities defined on a product of spaces, the existence statements in the literature require pseudomonotonicity of the operator, a hypothesis that is too strong for many applications, in particular in economics. On the other hand, the current minimal hypotheses for existence results for general quasi-variational inequalities are quasi-monotonicity and local upper sign-continuity. But since the product of quasi-monotone (respectively, locally upper sign-continuous) operators is not in general quasi-monotone (respectively, locally upper sign-continuous), it is thus quite difficult to use these general-type existence result in the quasi-variational inequalities defined on a product of spaces. In this work we prove, in an infinite-dimensional setting, several existence results for product-type quasi-variational inequalities by only assuming the quasi-monotonicity and local upper sign-continuity of the component operators. Our technique of proof is strongly based on an innovative stability result and on the new concept of net-lower sign-continuity

Optimal design of exchange networks with blind inputs and its application to Eco-industrial parks

Motivated by the design and optimization of the water exchange networks in Eco-Industrial Parks (EIP), we investigate the abstract Blind-Input model for general exchange networks. This abstract model is based on a Game Theory approach, formulating it as a Single-Leader-Multi-Follower (SLMF) game: at the upper level, there is an authority (leader) that aims to minimize the consumption of natural resources, while, at the lower level, agents (followers) try to minimize their operating costs. We introduce the notion of Blind-Input contract, which is an economic contract between the authority and the agents in order to ensure the participation of the latter ones in the exchange networks. More precisely, when participating in the exchange network, each agent accepts to have a blind input in the sense that she controls only her output fluxes, and the authority commits to guarantee a minimal relative improvement in comparison with the agent’s stand-alone operation. The SLMF game is equivalently transformed into a single mixed-integer optimization problem. Thanks to this reformulation, examples of EIP of realistic size are then studied numerically

Water integration in eco-industrial parks using a multi-leader-follower approach.

The design and optimization of industrial water networks in eco-industrial parks are studied by formulating and solving multi-leader-follower game problems. The methodology is explained by demonstrating its advantages against multi-objective optimization approaches. Several formulations and solution methods for MLFG are discussed in detail. The approach is validated on a case study of water integration in EIP without and with regeneration units. In the latter, multi-leader-single-follower and single-leader-multi-follower games are studied. Each enterprise's objective is to minimize the total annualized cost, while the EIP authority objective is to minimize the consumption of freshwater within the ecopark. The MLFG is transformed into a MOPEC and solved using GAMS® as an NLP. Obtained results are compared against the MOO approach and between different MLFG formulations. The methodology proposed is proved to be very reliable in multi-criteria scenarios compared to MOO approaches, providing numerical Nash equilibrium solutions and specifically in EIP design and optimization

Utility network optimization in eco-industrial parks by a multi-leader follower game methodology

A multi-leader-follower game (MLFG) model for the design of the utility network in an eco-industrial park (EIP) is studied and implemented by introducing the concept of an environmental authority. The methodology also considers the flowsheet simulation of each enterprise involved in the EIP in order to obtain utility consumption of each enterprise operating by itself. The approach is validated on a case study of a potential Norwegian EIP. In the latter, multi-leader-single-follower and single-leader-multi-follower game models are studied. Each enterprise's objective is to minimize the total annualized cost, while the EIP authority objective is to minimize the equivalent CO2 consumption related to utility consumption within the ecopark. The MLFG is transformed into a MOPEC and solved using GAMS® as an NLP. The methodology proposed is proven to be reliable in multi-criteria scenarios compared to traditional multiobjective optimization approaches, providing numerical Nash/Stackelberg equilibrium solutions and specifically in EIP planning and optimization

Rickettsial Infections and Fever, Vientiane, Laos

Rickettsia spp. are an underrecognized cause of undifferentiated febrile illness

Generalized Nash equilibrium problems, bilevel programming and mpec

The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November–6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considered as an application of calmness concept of multifunctions and is used to derive M-stationarity conditions for MPEC. Chapter 3 discusses the first- and second-order optimality conditions derived for a special case of a bilevel optimization problem in which the constraint set of the lower level problem is described as a general compact convex set. Chapter 4 concentrates the results of the modelization and analysis of deregulated electricity markets with a focus on auctions and mechanism design. Chapter 5 focuses on optimization approaches called reflection methods for protein conformation determination within the framework of matrix completion. The last chapter (Chap. 6) deals with the single-valuedness of quasimonotone maps by using the concept of single-directionality with a special focus on the case of the normal operator of lower semi-continuous quasiconvex functions

Sufficient conditions to compute any solution of a quasivariational inequality via a variational inequality

We define the concept of reproducible map and show that, whenever the constraint map defining the quasivariational inequality (QVI) is reproducible then one can characterize the whole solution set of the QVI as a union of solution sets of some variational inequalities (VI). By exploiting this property, we give sufficient conditions to compute any solution of a generalized Nash equilibrium problem (GNEP) by solving a suitable VI. Finally, we define the class of pseudo-Nash equilibrium problems, which are (not necessarily convex) GNEPs whose solutions can be computed by solving suitable Nash equilibrium problems. © 2016, Springer-Verlag Berlin Heidelberg