Search results for "Mathematical optimization"
showing 10 items of 1300 documents
A variational inequality approach to constrained control problems for parabolic equations
1988
A distributed optimal control problem for parabolic systems with constraints in state is considered. The problem is transformed to control problem without constraints but for systems governed by parabolic variational inequalities. The new formulation presented enables the efficient use of a standard gradient method for numerically solving the problem in question. Comparison with a standard penalty method as well as numerical examples are given.
Incremental heuristic approach for meter placement in radial distribution systems
2019
The evolution of modern power distribution systems into smart grids requires the development of dedicated state estimation (SE) algorithms for real-time identification of the overall system state variables. This paper proposes a strategy to evaluate the minimum number and best position of power injection meters in radial distribution systems for SE purposes. Measurement points are identified with the aim of reducing uncertainty in branch power flow estimations. An incremental heuristic meter placement (IHMP) approach is proposed to select the locations and total number of power measurements. The meter placement procedure was implemented for a backward/forward load flow algorithm proposed by…
Optimal Starting Conditions for the Rendezvous Maneuver, Part 2: Mathematical Programming Approach
2008
In a companion paper (Part 1, J. Optim. Theory Appl. 137(3), [2008]), we determined the optimal starting conditions for the rendezvous maneuver using an optimal control approach. In this paper, we study the same problem with a mathematical programming approach.
Necessary Optimality Conditions in Multiobjective Dynamic Optimization
2004
We consider a nonsmooth multiobjective optimal control problem related to a general preference. Both differential inclusion and endpoint constraints are involved. Necessary conditions and Hamiltonian necessary conditions expressed in terms of the limiting Frechet subdifferential are developed. Examples of useful preferences are given.
On necessary optimality conditions for optimal control problems governed by elliptic systems
2005
The article considers an optimal control problem for the linear elliptic system div for the case where the coefficient matrix A plays the role of control and belongs to a nonconvex set and the cost functional is a quadratic form with respect to . By transforming the original problem to a more suitable one and by using ideas from the homogenization theory a necessary optimality condition is derived.
A new preference handling technique for interactive multiobjective optimization without trading-off
2015
Because the purpose of multiobjective optimization methods is to optimize conflicting objectives simultaneously, they mainly focus on Pareto optimal solutions, where improvement with respect to some objective is only possible by allowing some other objective(s) to impair. Bringing this idea into practice requires the decision maker to think in terms of trading-off, which may limit the ability of effective problem solving. We outline some drawbacks of this and exploit another idea emphasizing the possibility of simultaneous improvement of all objectives. Based on this idea, we propose a technique for handling decision maker’s preferences, which eliminates the necessity to think in terms of t…
Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems
2015
This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed
Metric regularity and second-order necessary optimality conditions for minimization problems under inclusion constraints
1994
In this paper, we establish some general metric regularity results for multivalued functions on Banach spaces. Then, we apply them to derive second-order necessary optimality conditions for the problem of minimizing a functionf on the solution set of an inclusion 0?F(x) withx?C, whenF has a closed convex second-order derivative.
Error Estimates for a Class of Elliptic Optimal Control Problems
2016
In this article, functional type a posteriori error estimates are presented for a certain class of optimal control problems with elliptic partial differential equation constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state equation. The functional a posteriori error estimates developed by Repin in the late 1990s are applied to estimate the cost function value from both sides without requiring the exact solution of the state equation. Moreover, a lower bound for the minimal cost functional value is derived. A meaningful error quantity coinciding with the gap between the cost functional values of an arbitrary admissible …
Reliability-based design optimization of trusses under dynamic shakedown constraints
2019
A reliability-based design optimization problem under dynamic shakedown constraints for elastic perfectly plastic truss structures subjected to stochastic wind actions is presented. The simultaneous presence of quasi-static (cyclic) thermal loads is also considered. As usual in the shakedown theory, the quasi-statical loads will be defined as variable within a deterministic domain, while the dynamic problem will be treated considering an extended Ceradini-Gavarini approach. Some sources of uncertainties are introduced in the structural system and in the load definition. The reliability-optimization problem is formulated as the minimization of the volume of the structure subjected to determi…