We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distances. We propose a framework for the convergence analysis of the sequence generated by the algorithm. This class of problems is very interesting because it covers mathematical programs and optimization problems under equilibrium constraints. As an application, we consider the problem of the stability and change dynamics of a leader-follower relationship in a hierarchical organization.
In this paper, we introduce a new proximal algorithm for equilibrium problems on a genuine Hadamard manifold, using a new regularization term. We first extend recent existence results by considering pseudomonotone bifunctions and a weaker sufficient condition than the coer-civity assumption. Then, we consider the convergence of this proximal-like algorithm which can be applied to genuinely Hadamard manifolds and not only to specific ones, as in the recent literature. A striking point is that our new regularization term have a clear interpretation in a recent "variational rationality" approach of human behavior. It represents the resistance to change aspects of such human dynamics driven by motivation to change aspects. This allows us to give an application to the theories of desires, showing how an agent must escape to a succession of temporary traps to be able to reach, at the end, his desires.
Environmental legislation has placed constraints on the extraction of natural resources. As the construction industry is highly dependent on raw materials, more sustainable choices are required. This necessitates a cost-benefit analysis of the alternatives. Focusing on the benefits to the environment with the reduction of clay consumption, this work proposes an exploratory study on the production of unburned bricks with construction and demolition ceramic waste. The construction and demolition waste used was composed solely of ceramic brick remains, being crushed and sieved until reaching the desired granulometry to start the manufacturing process.Among three different properties, the bricks that obtained the best performance were those that incorporated higher content of construction and demolition ceramic waste.
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