MUSE-BB: A Decomposition Algorithm for Nonconvex Two-Stage Problems using Strong Multisection Branching

\(\) We present MUSE-BB, a branch-and-bound (B&B) based decomposition algorithm for the deterministic global solution of nonconvex two-stage stochastic programming problems. In contrast to three recent decomposition algorithms, which solve this type of problem in a projected form by nesting an inner B&B in an outer B&B on the first-stage variables, we branch on all … Read more

libDIPS — Discretization-Based Semi-Infinite and Bilevel Programming Solvers

We consider several hierarchical optimization programs: (generalized) semi-infinite and existence-constrained semi-infinite programs, minmax, and bilevel programs. Multiple adaptive discretization-based algorithms have been published for these program classes in recent decades. However, rigorous numerical performance comparisons between these algorithms are lacking. Indeed, if numerical comparisons are provided at all, they usually compare a small selection of … Read more

Adaptive discretization-based algorithms for semi-infinite programs with unbounded variables

The proof of convergence of adaptive discretization-based algorithms for semi-infinite programs (SIPs) usually relies on compact host sets for the upper- and lower-level variables. This assumption is violated in some applications, and we show that indeed convergence problems can arise when discretization-based algorithms are applied to SIPs with unbounded variables. To mitigate these convergence problems, … Read more

Optimal Eco-Routing for Hybrid Vehicles with Mechanistic/Data-Driven Powertrain Model Embedded

Hybrid Electric Vehicles (HEVs) are regarded as an important (transition) element of sustainable transportation. Exploiting the full potential of HEVs requires (i) a suitable route selection and (ii) suitable power management, i.e., deciding on the split between combustion engine and electric motor usage as well as the mode of the electric motor, i.e., driving or … Read more

Recent Advances in Nonconvex Semi-infinite Programming: Applications and Algorithms

The goal of this literature review is to give an update on the recent developments for semi-infinite programs (SIPs), approximately over the last 20 years. An overview of the different solution approaches and the existing algorithms is given. We focus on deterministic algorithms for SIPs which do not make any convexity assumptions. In particular, we … Read more

Global Dynamic Optimization with Hammerstein-Wiener Models Embedded

Hammerstein-Wiener models constitute a significant class of block-structured dynamic models, as they approximate process nonlinearities on the basis of input-output data without requiring identification of a full nonlinear process model. Optimization problems with Hammerstein-Wiener models embedded are nonconvex, and thus local optimization methods may obtain suboptimal solutions. In this work, we develop a deterministic global … Read more

Dynamic Optimization with Complementarity Constraints: Smoothing for Direct Shooting

We consider optimization of differential-algebraic equations (DAEs) with complementarity constraints (CCs) of algebraic state pairs. Formulating the CCs as smoothed nonlinear complementarity problem (NCP) functions leads to a smooth DAE, allowing for the solution in direct shooting. We provide sufficient conditions for well-posedness. Thus, we can prove that with the smoothing parameter going to zero, … Read more

Discretization-based algorithms for generalized semi-infinite and bilevel programs with coupling equality constraints

Discretization-based algorithms are proposed for the global solution of mixed-integer nonlinear generalized semi-infinite (GSIP) and bilevel (BLP) programs with lower-level equality constraints coupling the lower and upper level. The algorithms are extensions, respectively, of the algorithm proposed by Mitsos and Tsoukalas (J Glob Optim 61(1):1–17, 2015. https://doi.org/10.1007/s10898-014-0146-6) and by Mitsos (J Glob Optim 47(4):557–582, 2010. … Read more

Deterministic Global Optimization with Artificial Neural Networks Embedded

Artificial neural networks (ANNs) are used in various applications for data-driven black-box modeling and subsequent optimization. Herein, we present an efficient method for deterministic global optimization of ANN embedded optimization problems. The proposed method is based on relaxations of algorithms using McCormick relaxations in a reduced-space [\textit{SIOPT}, 20 (2009), pp. 573-601] including the convex and … Read more

Tighter McCormick Relaxations through Subgradient Propagation

Tight convex and concave relaxations are of high importance in the field of deterministic global optimization. We present a heuristic to tighten relaxations obtained by the McCormick technique. We use the McCormick subgradient propagation (Mitsos et al., SIAM J. Optim., 2009) to construct simple affine under- and overestimators of each factor of the original factorable … Read more