Month: January 2009

The Advanced Step NMPC Controller: Optimality, Stability and Robustness

  • Lorenz T. Biegler
  • Victor M. Zavala
    • Categories Control Applications, Nonlinear Optimization, Optimization of Systems modeled by PDEs

    Widespread application of dynamic optimization with fast optimization solvers leads to increased consideration of first-principles models for nonlinear model predictive control (NMPC). However, significant barriers to this optimization-based control strategy are feedback delays and consequent loss of performance and stability due to on-line computation. To overcome these barriers, recently proposed NMPC controllers based on nonlinear … Read more

    A Fast Moving Horizon Estimation Algorithm Based on Nonlinear Programming Sensitivity

  • Lorenz T. Biegler
  • Carl D. Laird
  • Victor M. Zavala
    • Categories Control Applications, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    Moving Horizon Estimation (MHE) is an efficient optimization-based strategy for state estimation. Despite the attractiveness of this method, its application in industrial settings has been rather limited. This has been mainly due to the difficulty to solve, in real-time, the associated dynamic optimization problems. In this work, a fast MHE algorithm able to overcome this … Read more

    Free Material Optimization with Fundamental Eigenfrequency Constraints.

  • Michal Kočvara
  • Günter Leugering
  • Michael Stingl
    • Categories Mechanical Engineering, Semi-definite Programming Tags , , ,

    The goal of this paper is to formulate and solve free material optimization problems with constraints on the smallest eigenfrequency of the optimal structure. A natural formulation of this problem as linear semidefinite program turns out to be numerically intractable. As an alternative, we propose a new approach, which is based on a nonlinear semidefinite … Read more

    A Logarithmic-Quadratic Proximal Point Scalarization Method for Multiobjective Programming

  • Ronaldo Malheiros Gregório
  • Paulo Roberto Oliveira
    • Categories Multi-Criteria Optimization Tags , ,

    We present a proximal point method to solve multiobjective problems based on the scalarization for maps. We build a family of a convex scalar strict representation of a convex map F with respect to the lexicographic order on Rm and we add a variant of the logarithmquadratic regularization of Auslender, where the unconstrained variables in … Read more

    On the Optimal On-Line Management of Photovoltaic-Hydrogen Hybrid Energy Systems

  • Mihai Anitescu
  • Victor M. Zavala
  • Theodore Krause
    • Categories Chemical Engineering, Control Applications, Stochastic Programming Tags , , , ,

    We present an on-line management strategy for photovoltaic-hydrogen (PV-H2) hybrid energy systems. The strategy follows a receding-horizon principle and exploits solar radiation forecasts and statistics generated through a Gaussian process model. We demonstrate that incorporating forecast information can dramatically improve the reliability and economic performance of these promising energy production devices. ArticleDownload View PDF

    A Nonstandard Simplex Algorithm for Linear Programming

  • Ping-Qi Pan
    • Categories Linear Programming Tags , , ,

    The simplex algorithm travels, on the underlying polyhedron, from vertex to vertex until reaching an optimal vertex. With the same simplex framework, the proposed algorithm generates a series of feasible points (which are not necessarily vertices). In particular, it is exactly an interior point algorithm if the initial point used is interior. Computational experiments show … Read more

    An interior point algorithm for nonlinear minimax problems

  • Enitan Obasanjo
  • Berc Rustem
  • George Tzallas-Regas
    • Categories Constrained Nonlinear Optimization Tags , , ,

    We present a primal-dual interior point method for constrained nonlinear, discrete minimax problems where the objective functions and constraints are not necessarily convex. The algorithm uses two merit functions to ensure progress towards the points satisfying the first order optimality conditions of the original problem. Convergence properties are described and numerical results provided. CitationDept. of … Read more

    The opportunistic replacement problem: analysis and case studies

  • Torgny Almgren
  • Niclas Andreasson
  • Adam Wojciechowski
  • Michael Patriksson
  • Ann-Brith Strömberg
    • Categories (Mixed) Integer Linear Programming, Scheduling Tags , , , , ,

    We consider an optimization model for determining optimal opportunistic maintenance (that is, component replacement) schedules when data is deterministic. This problem generalizes that of Dickman, Epstein, and Wilamowsky [21] and is a natural starting point for the modelling of replacement schedules when component lives are non-deterministic. We show that this basic opportunistic replacement problem is … Read more

    Nuclear norm minimization for the planted clique and biclique problems

  • Brendan Ames
  • Stephen A. Vavasis
    • Categories Combinatorial Optimization, Convex Optimization Tags , , , , ,

    We consider the problems of finding a maximum clique in a graph and finding a maximum-edge biclique in a bipartite graph. Both problems are NP-hard. We write both problems as matrix-rank minimization and then relax them using the nuclear norm. This technique, which may be regarded as a generalization of compressive sensing, has recently been … Read more

    Generic identifiability and second-order sufficiency in tame convex optimization

  • Jérôme Bolte
  • Aris Daniilidis
  • Adrian Lewis
    • Categories Convex Optimization Tags , , ,

    We consider linear optimization over a fixed compact convex feasible region that is semi-algebraic (or, more generally, “tame”). Generically, we prove that the optimal solution is unique and lies on a unique manifold, around which the feasible region is “partly smooth”, ensuring finite identification of the manifold by many optimization algorithms. Furthermore, second-order optimality conditions … Read more