Discrete optimization

About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.

Real-Time PDE-Constrained Optimization

Abstract: Preface Part I. Concepts and Properties of Real-Time, Online Strategies: 1. Constrained optimal feedback control for DAE 2. A stabilizing real-time implementation of NMPC 3. Numerical feedback controller design for PDE systems using model reduction: techniques and case studies 4. Least-squares methods for optimization Part II. Fast PDE-Constrained Optimization Solvers: 5. Space-time multigrid methods for solving unsteady optimal control problem 6. A time-parallel implicit methodology for the near-real-time solution of systems of linear oscillators 7. Generalized SQP-methods with 'parareal' time-domain decomposition for time-dependent PDE-constrained optimization 8. Simultaneous pseudo-timestepping for state constrained optimization problems in aerodynamics 9. The effect of the digital filter stepsize control on control optimization performance Part III. Reduced Order Modeling: 10. Certified rapid solution of partial differential equations for real-time parameter estimation and optimization 11. WillcoxMOR 12. Feedback control of flow separation Part IV. Applications: 13. Shape and topological sensitivity 14. COFIR: Coarse and fine image registration 15. Real-time, large scale optimization of water network systems using a subdomain approach Index.

A global approach for nonlinear mixed discrete programming in design optimization

Abstract: Most current nonlinear mixed discrete programs can only find locally optimal solutions. This paper proposes an optimization method to find the global solution of a nonlinear mixed discrete program. Based on the fact that: “For a discrete variable xi iff xi ∊{k1, k1, k2…,km } then (xi −k 1) (xi k 2)(xi km =0”, the original mixed discrete program is transformed into a penalty optimization program with continuous variables. This penalty optimization program is then solved to find a local optimum. Utilizing the Multi-Level Single Linkage technique, enough starting points are systematically generated to search for most local optima within the feasible region. A global optimum is then found at a pre-specified sufficiently high confidence level such as 99.5%. Some examples of design optimization in literature are tested, which demonstrate that the proposed method is superior to current methods for finding the global optimum.

Medium-term hydrothermal coordination by semidefinite programming

Abstract: Hydrothermal coordination (HTC) is a problem that has been solved using direct and decomposition solution methods. The latter has shown shorter solution times than the former. A direct solution method for the HTC problem that is based in semidefinite programming (SDP) is presented in this paper. SDP is a convex programming method with polynomial solution time. The variables of the problem are arranged in a vector, which is used to construct a positive-definite matrix; the optimal solution is then found in the cone defined by the set of positive-definite matrices. An HTC problem can be formulated as a convex optimization problem without explicitly stating the integer value requirements for the thermal-plants discrete variables. Thus, it is possible to replace the nonconvex integer-value constraints by convex quadratic constraints, and then use SDP. Due to its polynomial complexity, it is not necessary to use decomposition or other tools for discrete optimization, such as enumeration schemes or other exponential-time procedures. No initial relaxation is necessary when applying a SDP algorithm; the solution shows only minor mismatches in the integer variables, which are easily corrected by a heuristic method. Different size test cases are presented. The solution quality is assessed by comparing with that produced by a Lagrangian relaxation method.