Alexander Mitsos

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

    A Hybrid Discretization Algorithm with Guaranteed Feasibility for the Global Solution of Semi-Infinite Programs

  • Hatim Djelassi
  • Alexander Mitsos
    • Categories Semi-infinite Programming

    A discretization-based algorithm for the global solution of semi-infinite programs (SIPs) is proposed, which is guaranteed to converge to a feasible, ε-optimal solution finitely under mild assumptions. The algorithm is based on the hybridization of two existing algorithms. The first algorithm (Mitsos in Optimization 60(10–11):1291–1308, 2011) is based on a restriction of the right-hand side … Read more

    Global Optimization of Generalized Semi-Infinite Programs via Restriction of the Right Hand Side

  • Alexander Mitsos
  • Angelos Tsoukalas
    • Categories Global Optimization, Semi-infinite Programming

    The algorithm proposed in [Mitsos Optimization 2011] for the global optimization of semi-infinite programs is extended to the global optimization of generalized semi-infinite programs (GSIP). No convexity or concavity assumptions are made. The algorithm employs convergent lower and upper bounds which are based on regular (in general nonconvex) nonlinear programs (NLP) solved by a (black-box) … Read more

    Multi-Variate McCormick Relaxations

  • Alexander Mitsos
  • Angelos Tsoukalas
    • Categories Global Optimization Theory Tags , , , , , ,

    G. P. McCormick [Math Prog 1976] provides the framework for convex/concave relaxations of factorable functions, via rules for the product of functions and compositions of the form F(f(z)), where F is a univariate function. Herein, the composition theorem is generalized to allow multivariate outer functions F, and theory for the propagation of subgradients is presented. … Read more