Optimal guidance law development for an advanced launch system

A regular perturbation analysis is presented. Closed-loop simulations were performed with a first order correction including all of the atmospheric terms. In addition, a method was developed for independently checking the accuracy of the analysis and the rather extensive programming required to implement the complete first order correction with all of the aerodynamic effects included. This amounted to developing an equivalent Hamiltonian computed from the first order analysis. A second order correction was also completed for the neglected spherical Earth and back-pressure effects. Finally, an analysis was begun on a method for dealing with control inequality constraints. The results on including higher order corrections do show some improvement for this application; however, it is not known at this stage if significant improvement will result when the aerodynamic forces are included. The weak formulation for solving optimal problems was extended in order to account for state inequality constraints. The formulation was tested on three example problems and numerical results were compared to the exact solutions. Development of a general purpose computational environment for the solution of a large class of optimal control problems is under way. An example, along with the necessary input and the output, is given

The best, the worst and the semi-strong: optimal values in interval linear programming

Interval programming provides one of the modern approaches to modeling optimization problems under uncertainty. Traditionally, the best and the worst optimal values determining the optimal value range are considered as the main solution concept for interval programs. In this paper, we present the concept of semi-strong values as a generalization of the best and the worst optimal values. Semi-strong values extend the recently introduced notion of semi-strong optimal solutions, allowing the model to cover a wider range of applications. We propose conditions for testing values that are strong with respect to the objective vector, right-hand-side vector or the constraint matrix for interval linear programs in the general form.</p

Strong Duality for a Multiple-Good Monopolist

We characterize optimal mechanisms for the multiple-good monopoly problem and provide a framework to find them. We show that a mechanism is optimal if and only if a measure $\mu$ derived from the buyer's type distribution satisfies certain stochastic dominance conditions. This measure expresses the marginal change in the seller's revenue under marginal changes in the rent paid to subsets of buyer types. As a corollary, we characterize the optimality of grand-bundling mechanisms, strengthening several results in the literature, where only sufficient optimality conditions have been derived. As an application, we show that the optimal mechanism for $n$ independent uniform items each supported on $[c,c+1]$ is a grand-bundling mechanism, as long as $c$ is sufficiently large, extending Pavlov's result for $2$ items [Pavlov'11]. At the same time, our characterization also implies that, for all $c$ and for all sufficiently large $n$, the optimal mechanism for $n$ independent uniform items supported on $[c,c+1]$ is not a grand bundling mechanism

General models in min-max planar location

This paper studies the problem of deciding whether the present iteration point of some algorithm applied to a planar singlefacility min-max location problem, with distances measured by either anl p -norm or a polyhedral gauge, is optimal or not. It turns out that this problem is equivalent to the decision problem of whether 0 belongs to the convex hull of either a finite number of points in the plane or a finite number of differentl q -circles . Although both membership problems are theoretically solvable in polynomial time, the last problem is more difficult to solve in practice than the first one. Moreover, the second problem is solvable only in the weak sense, i.e., up to a predetermined accuracy. Unfortunately, these polynomial-time algorithms are not practical. Although this is a negative result, it is possible to construct an efficient and extremely simple linear-time algorithm to solve the first problem. Moreover, this paper describes an implementable procedure to reduce the second decision problem to the first with any desired precision. Finally, in the last section, some computational results for these algorithms are reported.optimality conditions;continuous location theory;computational geometry;convex hull;Newton-Raphson method