We consider the linear-quadratic optimal control problem for a controlled differential algebraic equation (DAE). Under minimal assumptions on the DAE concerning index and regularity it will be possible to prove that the sufficient optimality condition given in papers of G. Kurina and R. März is also a necessary condition. This condition includes the solution of an appropriate boundary value pro...

To devise efficient solutions for approximating a mean partition in consensus clustering, Dimitriadou et al. [3] presented a necessary condition of optimality for a consensus function based on least square distances. We show that their result is pivotal for deriving interesting properties of consensus clustering beyond optimization. For this, we present the necessary condition of optimality in ...

There are various families of Learning Automata (LA) such as Fixed Structure, Variable Structure, Discretized etc. Informally, if the environment is stationary, their ε-optimality is defined as their ability to converge to the optimal action with an arbitrarily large probability, if the learning parameter is sufficiently small/large. Of these LA families, Estimator Algorithms (EAs) are certainl...

We study a trust region affine scaling algorithm for solving the linearly constrained convex or concave programming problem. Under primal nondegeneracy assumption, we prove that every accumulation point of the sequence generated by the algorithm satisfies the first order necessary condition for optimality of the problem. For a special class of convex or concave functions satisfying a certain in...

This paper investigates the necessary conditions of optimality for uniformly overtaking optimal control on infinite horizon with free right endpoint. Clarke’s form of the Pontryagin Maximum Principle is proved without the assumption on boundedness of total variation of adjoint variable. The transversality condition for adjoint variable is shown to become necessary if the adjoint variable is par...

Abstract: Avella et al. (2006) [Avella, P., D’Auria, B., Salerno, S. (2006). A LP-based heuristic for a time-constrained routing problem. European Journal of Operational Research 173:120-124] investigate a timeconstrained routing (TCR) problem. The core of the proposed solution approach is a large-scale linear program (LP) that grows both rowand column-wise when new variables are introduced. Th...

A powerful approach for analyzing the stability of continuous–time switched systems is based on using optimal control theory to characterize the “most unstable” switching law. This reduces the problem of determining stability under arbitrary switching to analyzing stability for the specific “most unstable” switching law. For discrete–time switched systems, the variational approach received cons...

A multi-objective heuristic particle swarm optimiser (MOHPSO) based on Pareto multi-objective theory is proposed to solve multi-objective optimality problems. The optimality objectives are the roof displacement and structure weight. Two types of structure are analysed in this paper, a truss structure and a framework structure. Performance-based seismic analysis, such as classical and modal push...

Applications in constrained optimization (and other areas) produce symmetric matrices with a natural block 2 2 structure. An optimality condition leads to the problem of perturbing the (1,1) block of the matrix to achieve a speci®c inertia. We derive a perturbation of minimal norm, for any unitarily invariant norm, that increases the number of nonnegative eigenvalues by a given amount, and we s...

This paper focuses on the development of optimality conditions for a bilevel optimal control problem with pure state constrains in the upper level and a finite-dimensional parametric optimization problem in the lower level. After transforming the problem into an equivalent single-level problem we concentrate on the derivation of a necessary optimality condition of Pontryagin-type. We point out ...