Alexander Mitsos

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

  • Aron Zingler
  • Alexander Mitsos
  • Daniel Jungen
  • Hatim Djelassi
    • Categories Optimization Software and Modeling Systems, Robust Optimization, Semi-infinite Programming Tags , , , , ,

    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

  • Daniel Jungen
  • Hatim Djelassi
  • Alexander Mitsos
    • Categories Global Optimization Tags , ,

    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

  • Adrian Caspari
  • Alexander Mitsos
  • Steffen Fahr
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Transportation Tags , , , , , ,

    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

  • Hatim Djelassi
  • Alexander Mitsos
  • Oliver Stein
    • Categories Global Optimization Applications, Semi-infinite Programming

    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

  • D. Bongartz
  • Alexander Mitsos
  • Jaromił Najman
  • C. D. Kappatou
  • S. Sass
    • Categories Global Optimization Theory Tags , , , ,

    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

  • Lorenz T. Biegler
  • Adrian Caspari
  • Alexander Mitsos
  • Pascal Schäfer
  • Lukas Lüken
  • Adel Mhamdi
  • Yannic Vaupel
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    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

  • Hatim Djelassi
  • Alexander Mitsos
  • Moll Glass
    • Categories Global Optimization Applications, Global Optimization Theory, Semi-infinite Programming

    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

  • Alexander Mitsos
  • Artur M Schweidtmann
    • Categories Chemical Engineering, Global Optimization, Nonlinear Optimization Tags , , , , , , ,

    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

  • Alexander Mitsos
  • Jaromił Najman
    • Categories Global Optimization, Global Optimization Applications, Global Optimization Theory

    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

    Optimal Deterministic Algorithm Generation

  • Ioannis G. Kevrekidis
  • Alexander Mitsos
  • Jaromił Najman
    • Categories Applications - Science and Engineering, Global Optimization, Other Topics Tags , ,

    A formulation for the automated generation of algorithms via mathematical programming (optimization) is proposed. The formulation is based on the concept of optimizing within a parameterized family of algorithms, or equivalently a family of functions describing the algorithmic steps. The optimization variables are the parameters – within this family of algorithms- that encode algorithm design: … Read more