### 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.

##### 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).

##### 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.

##### 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.

##### 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.