Nonlinear programming is a very important tool for optimizing many systems in science and engineering. The interior point solver IPOPT has become one of the most popular solvers for NLP because of its high performance. However, certain types of problems are still challenging for IPOPT. This dissertation considers three improvements or extensions to IPOPT to improve performance on several practical classes of problems. Compared to active set solvers that treat inequalities by identifying active constraints and transforming to equalities, the interior point method is less robust in the presence of degenerate constraints. Interior point methods require certain regularity conditions on the constraint set for the solution path to exist. Dependent constraints commonly appear in applications such as chemical process models and violate the regularity conditions. The interior point solver IPOPT introduces regularization terms to attempt to correct this, but in some cases the required regularization terms either too large or too small and the solver will fail. To deal with these challenges, we present a new structured regularization algorithm, which is able to numerically delete dependent equalities in the KKT matrix. Numerical experiments on hundreds of modified example problems show the effectiveness of this approach with average reduction of more than 50% of the iterations. In some contexts such as online optimization, very fast solutions of an NLP are very important. To improve the performance of IPOPT, it is best to take advantage of problem structure. Dynamic optimization problems are often called online in a control or stateestimation. These problems are very large and have a particular sparse structure. This work investigates the use of parallelization to speed up the NLP solution. Because the KKT factorization is the most expensive step in IPOPT, this is the most important step to parallelize. Several cyclic reduction algorithms are compared for their performance on generic test matrices as well as matrices of the form found in dynamic optimization. The results show that for very large problems, the KKT matrix factorization time can be improved by a factor of four when using eight processors. Mathematical programs with complementarity constraints (MPCCs) are another challenging class of problems for IPOPT. Several algorithmic modifications are examined to specially handle the difficult complementarity constraints. First, two automatic penalty adjustment approaches are implemented and compared. Next, the use of our structured regularization is tested in combination with the equality reformulation of MPCCs. Then, we propose an altered equality reformulation of MPCCs which effectively removes the degenerate equality or inequality constraints. Using the MacMPEC test library and two applications, we compare the efficiency of our approaches to previous NLP reformulation strategies.

In South Africa, certain areas are well developed with infrastructures that compare with first world standards, while in others, people live in abject poverty without basic services being rendered Poverty is the single greatest burden of South Africa's people. It is defined as the inability to meet a specified set of basic needs. This means that apart from low income levels, malnutrition and hunger, poverty manifests itself in poor people's lives in many other ways, including lack of access to basic social services. Poverty is characterized by the inability of individuals, households or communities to command sufficient resources to satisfy a socially acceptable minimum standard of living. It is perceived by poor South Africans themselves to include alienation from the community, food insecurity, crowded homes, usage of unsafe and inefficient forms of energy and lack of jobs that are adequately paid and I or secure. Because the government doesn't want to alienate those it is trying to serve, public services are being brought closer to people, so as to improve the quality of community life. The underlying reason for the implementation of Multi-purpose Community Centres (MPCCs) is to bring government services closer to people and to provide the community with the opportunity to communicate with government. Multi-Purpose Community Centres have been identified as the primary approach for the implementation of development communication and information programmes. MPCCs also serve as a base from which a wide range of services and products can reach communities. The aim is for communities to access such services and engage in government programmes for their own empowerment. As a result, MPPCs are a necessary poverty alleviation strategy that needs to be promoted for the improvement of the quality of community life. / Thesis (M. Development and Management)--North-West University, Potchefstroom Campus, 2006.

In South Africa, certain areas are well developed with infrastructures that compare with first world standards, while in others, people live in abject poverty without basic services being rendered Poverty is the single greatest burden of South Africa's people. It is defined as the inability to meet a specified set of basic needs. This means that apart from low income levels, malnutrition and hunger, poverty manifests itself in poor people's lives in many other ways, including lack of access to basic social services. Poverty is characterized by the inability of individuals, households or communities to command sufficient resources to satisfy a socially acceptable minimum standard of living. It is perceived by poor South Africans themselves to include alienation from the community, food insecurity, crowded homes, usage of unsafe and inefficient forms of energy and lack of jobs that are adequately paid and I or secure. Because the government doesn't want to alienate those it is trying to serve, public services are being brought closer to people, so as to improve the quality of community life. The underlying reason for the implementation of Multi-purpose Community Centres (MPCCs) is to bring government services closer to people and to provide the community with the opportunity to communicate with government. Multi-Purpose Community Centres have been identified as the primary approach for the implementation of development communication and information programmes. MPCCs also serve as a base from which a wide range of services and products can reach communities. The aim is for communities to access such services and engage in government programmes for their own empowerment. As a result, MPPCs are a necessary poverty alleviation strategy that needs to be promoted for the improvement of the quality of community life. / Thesis (M. Development and Management)--North-West University, Potchefstroom Campus, 2006.

Real-time optimization (RTO) is a supervisory strategy in the hierarchical industrial process automation architecture in which economically optimal set-point targets are computed for the lower level advanced control system, which is typically model predictive control (MPC). Due to highly volatile market conditions, recent developments have considered transforming the conventional steady-state RTO to dynamic RTO (DRTO) to permit economic optimization during transient operation. Published DRTO literature optimizes plant input trajectories without taking into account the presence of the plant control system, constituting an open-loop DRTO (OL-DRTO) approach. The goal of this research is to develop a design framework for a DRTO system that optimizes process economics based on a closed-loop response prediction. We focus, in particular, on DRTO applied to a continuous process operation regulated under constrained MPC. We follow a two-layer DRTO/MPC configuration due to its close tie to the industrial process automation architecture. We first analyze the effects of optimizing MPC closed-loop response dynamics at the DRTO level. A rigorous DRTO problem structure proposed in this thesis is in the form of a multilevel dynamic optimization problem, as it embeds a sequence of MPC optimization subproblems to be solved in order to generate the closed-loop prediction in the DRTO formulation, denoted here as a closed-loop DRTO (CL-DRTO) strategy. A simultaneous solution approach is applied in which the convex MPC optimization subproblems are replaced by their necessary and sufficient, Karush-Kuhn-Tucker (KKT) optimality conditions, resulting in the reformulation of the original multilevel problem as a single-level mathematical program with complementarity constraints (MPCC) with the complementarities handled using an exact penalty formulation. Performance analysis is carried out, and process conditions under which the CL-DRTO strategy significantly outperforms the traditional open-loop counterpart are identified. The multilevel DRTO problem with a rigorous inclusion of the future MPC calculations significantly increases the size and solution time of the economic optimization problem. Next, we identify and analyze multiple closed-loop approximation techniques, namely, a hybrid formulation, a bilevel programming formulation, and an input clipping formulation applied to an unconstrained MPC algorithm. Performance analysis based on a linear dynamic system shows that the proposed approximation techniques are able to substantially reduce the size and solution time of the rigorous CL-DRTO problem, while largely retaining its original performance. Application to an industrially-based case study of a polystyrene production described by a nonlinear differential-algebraic equation (DAE) system is also presented. Often large-scale industrial systems comprise multi-unit subsystems regulated under multiple local controllers that require systematic coordination between them. Utilization of closed-loop prediction in the CL-DRTO formulation is extended for application as a higher-level, centralized supervisory control strategy for coordination of a distributed MPC system. The advantage of the CL-DRTO coordination formulation is that it naturally considers interaction between the underlying MPC subsystems due to the embedded controller optimization subproblems while optimizing the overall process dynamics. In this case, we take advantage of the bilevel formulation to perform closed-loop prediction in two DRTO coordination schemes, with variations in the coordinator objective function based on dynamic economics and target tracking. Case study simulations demonstrate excellent performance in which the proposed coordination schemes minimize the impact of disturbance propagation originating from the upstream subsystem dynamics, and also reduce the magnitude of constraint violation through appropriate adjustment of the controller set-point trajectories. / Thesis / Doctor of Philosophy (PhD)