Optimal control is concerned with achieving a desired outcome, not by manipulating the path that can be taken within a specific system, but by manipulating the forces, or controls, that are fundamental to the system. It has no doubt been shown in the previous paper in this SSP series that optimal control problems are expressed using the functional, J, which serves as the performance index, in t...

This work provides necessary conditions for optimality in problems of optimal control expressed as instances of the Generalized Problem of Bolza, with the added feature that the fundamental planning interval is allowed to vary. A central product of the analysis is a generalization of the conservation-of-Hamiltonian condition for problems on either fixed or variable intervals. The results allow ...

There is a new field emerging around issues concerning the aggregation of a collection of individual “judgments” of a group of agents. An individual “judgment” is represented by a set of sentences in some logical language. One looks for a procedure that has as its output a “social” judgment. A key result in this area is List and Pettit’s impossibility result [13]. By generalizing the well-known...

Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is caused by regular variation of components of the original random structure. In this paper we build up on previous work and derive results in t...

Simple and analytically tractable expressions for functional determinants are known to exist for many cases of interest. We extend the range of situations for which these hold to cover systems of self-adjoint operators of the Sturm-Liouville type with arbitrary linear boundary conditions. The results hold whether or not the operators have negative eigenvalues. The physically important case of f...

We present a unified heuristic which is able to solve five different variants of the vehicle routing problem: the vehicle routing problem with time windows (VRPTW), the capacitated vehicle routing problem (CVRP), the multi-depot vehicle routing problem (MDVRP), the site-dependent vehicle routing problem (SDVRP) and the open vehicle routing problem (OVRP). All problemvariants are transformed int...

The paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function. Special cases in our approach include marginal models for longitudinal or clustered data, conditional logistic regression for matched case–control studies, multivariate measurement error models, generalized linear mixed models with a...

We present a general framework for vector assignment problems. In such problems one aims at assigning n input vectors to m machines such that the value of a given target function is minimized. While previous approaches concentrated on simple target functions such as max-max, the general approach presented here enables us to design a PTAS for a wide class of target functions. In particular we ar...

The paper is devoted to general elliptic problems in the Douglis-Nirenberg sense. We obtain a necessary and sufficient condition of normal solvability in the case of unbounded domains. Along with the ellipticity condition, proper ellipticity and Lopatinsky condition that determine normal solvability of elliptic problems in bounded domains, one more condition formulated in terms of limiting prob...