Path constraints arise naturally in dynamic optimization within chemical and biological processes due to process safety, environmental regulations, or critical quality attributes. Thus, they must be satisfied which poses a substantial challenge because of the continuous domain. It makes the optimization problem infinitely constrained. This work addresses this type of optimization problem and different algorithms are proposed to compute feasible solutions. The importance of satisfying path constraints is demonstrated in an experimental study using the algorithm proposed by Fu et al. [1]. Optimal feed rates are computed offline to maximize the mass of polystyrene produced in a fed-bath reactor. The concentration of monomer in the particles is constrained. Respecting this constraint over the whole time enables the operation of the reactor at a higher reaction rate, avoiding the accumulation of unreacted monomer in the reactor that may react hazardously at the end of the reaction. The computational results are validated by laboratory experiments. One of the main drawbacks of existing algorithms that calculate guaranteed feasible solutions is the number of iterations required. Each iteration often consists of a solution of a nonlinear program (NLP), resulting in high computational time. A new algorithm is proposed based on polynomial approximation of the path constraint. It computes solutions that do not violate the path constraint and terminates in a finite number of iterations. The algorithm is tested in four case studies. The results show that a solution is computed after few iterations by solving more complex NLPs, i.e., with more constraints. The algorithm can be applied to systems described by ordinary differential equations or differential-algebraic equations. Thus, constraints that need to be respected over a multidimensional space are not covered. A second algorithm based on Fu et al. [1] is proposed to address this type of constraint for systems described by partial differential equations (PDEs). The method takes into account the error of numerical solution of PDEs and guarantees constraints are not violated at any point in time and space. However, it requires the solution of many NLPs and PDEs, being computationally expensive. Therefore, the application to complex system may be not feasible with current computational power. Uncertain parameters may turn the solutions infeasible in practice. In the final part of this dissertation, a third algorithm is proposed to overcome this problem. It works for uncertain variables modelled by Gaussian distributions. The path constraint is formulated as a chance constraint and is enforced for a user-defined tolerance. Although the algorithm computes a solution that respects the chance constraint, results from two simple case studies show that the solution may be too conservative.