Existence of Local Saddle Points for a New Augmented Lagrangian Function

We give a new class of augmented Lagrangian functions for nonlinear programming problem with both equality and inequality constraints. The close relationship between local saddle points of this new augmented Lagrangian and local optimal solutions is discussed. In particular, we show that a local saddle point is a local optimal solution and the converse is also true under rather mild conditions

Multiobjective Optimization for Complex Systems

Complex systems are becoming more and more apparent in a variety of disciplines, making solution methods for these systems valuable tools. The solution of complex systems requires two significant skills. The first challenge of developing mathematical models for these systems is followed by the difficulty of solving these models to produce preferred solutions for the overall systems. Both issues are addressed by this research. This study of complex systems focuses on two distinct aspects. First, models of complex systems with multiobjective formulations and a variety of structures are proposed. Using multiobjective optimization theory, relationships between the efficient solutions of the overall system and the efficient solutions of its subproblems are derived. A system with a particular structure is then selected and further analysis is performed regarding the connection between the original system and its decomposable counterpart. The analysis is based on Kuhn-Tucker efficiency conditions. The other aspect of this thesis pertains to the study of a class of complex systems with a structure that is amenable for use with analytic target cascading (ATC), a decomposition and coordination approach of special interest to engineering design. Two types of algorithms are investigated. Modifications to a subgradient optimization algorithm are proposed and shown to improve the speed of the algorithm. A new family of biobjective algorithms showing considerable promise for ATC-decomposable problems is introduced for two-level systems, and convergence results for a specified algorithm are given. Numerical examples showing the effectiveness of all algorithms are included

Desenvolvimento de um modelo computacional para o problema da programação diária da operação de sistemas hidrotérmicos

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Elétrica, Florianópolis, 2010O problema da programação diária da operação de sistemas hi-drotérmicos tem como objetivo definir quais unidades devem estar operando, os respectivos níveis de geração, em cada hora do dia seguinte, com o propósito de atender à demanda ao longo do dia, às restrições operativas das usinas e dos reservatórios e às restrições elétricas do sistema ao menor custo operativo. Uma característica desafiante do problema da programação consiste em obter uma solução de boa qualidade com um custo computa-cional moderado. A obtenção de uma solução dessa natureza requer uma modelagem detalhada de todos os elementos de ge-ração e transmissão do sistema hidrotérmico. Em consequência, o problema de otimização resultante possui um elevado grau de complexidade, o qual pode ser decomposto em subproblemas menores, com características distintas e mais fáceis de serem so-lucionados. Neste trabalho, a estratégia de solução proposta para o problema da programação diária está baseada nas metodologi-as da Relaxação Lagrangeana e do Lagrageano Aumentado. Essa estratégia de solução proposta para o problema da programação diária é analisada em uma configuração hidrotérmica, extraída do sistema elétrico brasileiro.The daily operation programming problem of hydrothermal systems aims to define which units should be in operation, the respective generation levels at each hour of the day, with the purpose of matching the demand, and meeting the operating plants constraints, the reservoir constraints and the electrical system constraints at the minimum operative cost. A challenging feature of this programming problem consists of obtaining a solution with good quality and moderate computational burden. In order to obtain a good solution, a detailed modeling of the generation and the transmission system is required. Consequently, the resulting optimization problem has a high degree of complexity, which can be decomposed into smaller subproblems, with distinctive characteristics and easier to solve. In this work, the proposed strategy of solution to the daily programming problem is based on the Lagrangian Relaxation and Augmented Lagrangian methods. This proposed strategy to the daily programming problem is analyzed in a hydrothermal setting, extracted from the Brazilian electrical system