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We present a deterministic global optimization method for nonlinear programming formulations constrained by stiff systems of ordinary differential equation (ODE) initial value problems (IVPs). The examples arise from dynamic optimization problems exhibiting both fast and slow transient phenomena commonly encountered in model‐based systems engineering applications. The proposed approach utilizes unconditionally stable implicit integration methods to reformulate the ODE‐constrained problem into a nonconvex nonlinear program (NLP) with implicit functions embedded. This problem is then solved to global optimality in finite time using a spatial branch‐and‐bound framework utilizing convex/concave relaxations of implicit functions constructed by a method which fully exploits problem sparsity. The algorithms were implemented in the Julia programming language within the EAGO.jl package and demonstrated on five illustrative examples with varying complexity relevant in process systems engineering. The developed methods enable the guaranteed global solution of dynamic optimization problems with stiff ODE–IVPs embedded.

 

Ion selective electrode (ISE) sensors have been broadly applied for real-time in situ monitoring of ion concentrations in water environments. However, ISE sensors suffer from critical problems, such as ionophore leaching, water-penetration, poor electrochemical stability, and resulting short life spans. In this study, a template-guided membrane matrix immobilization strategy was pursued as a novel ISE sensor fabrication methodology to enhance its sensing characteristics and longevity. Specifically, nano-porous anodized aluminum oxide (AAO) was used as the template for an NH 4 + -specific ISE sensor. A nano-porous nickel mesh eventually replaced the template and formed a compact, high-surface juncture with the NH 4 + ion-selective membrane matrix. The resulting template-guided nano-mesh ISE (TN-ISE) sensor displayed enhanced electrochemical stability ( i.e. , capacitance increased by 50%, reading drift reduced by 75%) when compared to a regular single-wall carbon nanotube (SW-CNT) ISE sensor used as the standard. The interface between the nano-mesh electrode and the ion selective membrane matrix was compact enough to prevent water influx at the electrode interface. This minimized ionophore leaching and increased the mechanical integrity of the TN-ISE sensor. The practical advantages of the novel sensor were validated via long-term (360 hours) tests in real wastewater, returning a small average error of 1.28% over this time. The results demonstrate the feasibility of the template-guided nano-mesh design and fabrication strategy toward ISEs for long-term continuous monitoring of water or wastewater quality.