Heuristic pattern search for bound constrained minimax problems

This paper presents a pattern search algorithm and its hybridization with a random descent search for solving bound constrained minimax problems. The herein proposed heuristic pattern search method combines the Hooke and Jeeves (HJ) pattern and exploratory moves with a randomly generated approxi- mate descent direction. Two versions of the heuristic algorithm have been applied to several benchmark minimax problems and compared with the original HJ pat- tern search algorithm

A Nonlinear Lagrange Algorithm for Stochastic Minimax Problems Based on Sample Average Approximation Method

An implementable nonlinear Lagrange algorithm for stochastic minimax problems is presented based on sample average approximation method in this paper, in which the second step minimizes a nonlinear Lagrange function with sample average approximation functions of original functions and the sample average approximation of the Lagrange multiplier is adopted. Under a set of mild assumptions, it is proven that the sequences of solution and multiplier obtained by the proposed algorithm converge to the Kuhn-Tucker pair of the original problem with probability one as the sample size increases. At last, the numerical experiments for five test examples are performed and the numerical results indicate that the algorithm is promising

Distributed self-tuning of sensor networks

This work is motivated by the need for an ad hoc sensor network to autonomously optimise its performance for given task objectives and constraints. Arguing that communication is the main bottleneck for distributed computation in a sensor network we formulate two approaches for optimisation of computing rates. The first is a team problem for maximising the minimum communication throughput of sensors and the second is a game problem in which cost for each sensor is a measure of its communication time with its neighbours. We investigate adaptive algorithms using which sensors can tune to the optimal channel attempt rates in a distributed fashion. For the team problem, the adaptive scheme is a stochastic gradient algorithm derived from the augmented Lagrangian formulation of the optimisation problem. The game formulation not only leads to an explicit characterisation of the Nash equilibrium but also to a simple iterative scheme by which sensors can learn the equilibrium attempt probabilities using only the estimates of transmission and reception times from their local measurements. Our approach is promising and should be seen as a step towards developing optimally self-organising architectures for sensor networks

Control of the Reservoirs System During Flood: Concept of Learning in Multi-Stage Decision Process

Although floods are not the strongest or the most sudden physical phenomena in the world, they appear to be one of the most disastrous events. During the last few decades we observed an unusual frequency of flood events. Examples of enormous flood damages in Poland in 1997, in Germany, the Czech Republic and Slovakia in 2002, and also in China, the United States, Southern Africa and many other countries are well known. It could be said that floods have become of the main development barriers for countries which are unable to cope with this problem. In the presence of extreme floods proper water management strategies have become dramatically important. Flood protection in the catchment scale requires application of efficient decision support system. However, the uncertainty linked to the unknown inflows scenarios makes this problem extremely difficult. In the report the possible structure of a decision support tool is presented. The elements of the system are discussed and some examples from the Nysa Klodzka reservoir system are given

Theoretical and numerical analysis of optimization problems with applications to continuum mechanics

Tese de doutoramento, Matemática (Análise Numérica e Matemática Computacional), Universidade de Lisboa, Faculdade de Ciências, 2013Fundação para a Ciência e a Tecnologia (FCT, Financiamento Base 2010 - ISFL/1/209, SFRH/BD/44343/2008); Mathematical and Numerical Methods in Mechanics research group do Centro de Matemática e Aplicações Fundamental da U

A smooth method for the finite minimax problem

We consider unconstrained minimax problems where the objective function is the maximum of a finite number of smooth functions. We prove that, under usual assumptions, it is possible to construct a continuously differentiable function, whose minimizers yield the minimizers of the max function and the corresponding minimum values. On this basis, we can define implementable algorithms for the solution of the minimax problem, which are globally convergent at a superlinear convergence rate. Preliminary numerical results are reported