Sumários

Strategies for global optimization of MINLPs

20 dezembro 2018, 09:30 • Pedro Castro

Two-stage MILP/NLP decomposition algorithms for MIQCPs. Spatial brand-and-bound for general problems.

Alternative formulations to a problems.
Multiperiod blending of refined petroleum products (MINLP formulation). Solving one such problem in GAMS.

Design of wastewater treatment networks

17 dezembro 2018, 09:30 • Pedro Castro

Mixed-integer quadratically constrained problems (MIQCPs) as an important class of mixed-integer nonlinear programming problems (MINLPs). Relaxation techniques for non-convex bilinear terms: (I) McCormick envelopes (LP relaxation); (ii) Piecewise McCormick envelopes (MILP); (iii) Multiparametric Disaggregation (MILP).

The wastewater treatment network (WTN) design problem. NLP formulation and its three relaxation models (of different strengths). Illustration by solving a WTN problem in GAMS. Comparison of performance to commercial global optimization solver BARON.

Design of water-using networks

13 dezembro 2018, 09:30 • Pedro Castro

Difficulties associated to nonlinear problems. NLP formulation for the design of water using networks featuring non-convex bilinear terms in the mass balances.

Avoiding circular references in networks with recycling.
Implementing and solving the water-using network design problem for a multicontaminant system in Excel. 

Karush-Kuhn-Tucker Optimality Conditions

10 dezembro 2018, 09:30 • Pedro Castro

Constrained optimisation. Feasibility region. Convex optimization problem. Comparison between linear, convex and non-convex optimization problems. Lagrangean function as a way to transform the problem into one without restrictions. Multipliers of equality and inequality constraints. Kinematic interpretation of Karush-Kuhn Tucker optimality conditions.

Exercises (pen and paper).

Optimization of functions in Rn without restrictions

6 dezembro 2018, 09:30 • Pedro Castro

Properties of matrices (e.g. eigenvalues), gradient vector and Hessian matrix.

Concepts of local/global optimum and convexity.
Stationary points, necessary and sufficient conditions for local optimality.
Exercises (pen and paper).