Polyhedral cutting-plane algorithms for hard combinatorial problems have scored notable successes. However, computational research on the Maximum-Weight Cut Problem (MCP) on undirected graphs has been inconclusive. In 1988, ...

This thesis studies problems derived from nonlinear partial differential equations of parabolic type. Part I. A mass reducing flow for integral currents. A mass reducing flow of integral current is constructed. The current ...

This thesis is a study of harmonic maps of trivalent trees into Euclidean space. The existence of such maps is established, and uniqueness is shown to hold up to a certain isotopy condition. Moreover, within its particular ...

In part I of this thesis, we prove some regularity and uniqueness results of the minimizer for the problem$$\inf\{\int\sb\Omega \phi(Dv) + \int\sb{\partial\Omega} \vert{v - g}\vert dH\sp{n-1} : v \in BV(\Omega), g \in ...

Many physical processes such as reflection seismology, oil exploration, and ground-penetrating radar may be modeled as inverse problems for the multidimensional acoustic wave equation with point energy sources. The inverse ...

In this research we study the role of indicator functions in the identification and the removal of zero variables in linear programming. The definition and desired properties of the indicators are given. We investigate the ...

This work concerns efficiently solving a class of nonlinear integer programming problems: min $\{f(x)$: $x \in \{0,1\}\sp{n}\}$ where $f(x)$ is a general nonlinear function. The notion of subgradient for the objective ...

In a recent paper, Barzilai and Borwein presented a new choice of steplength for the gradient method. Their choice does not guarantee descent in the objective function and greatly speeds up the convergence of the method. ...

Two new updates are presented, the UHU update and a modified Gurwitz update, for approximating the Hessian of the Lagrangian in nonlinear constrained optimization problems. Under the standard assumptions, the new UHU ...

Let compact n-dimensional Riemannian manifolds $(M,g),\ (\widehat M,\ g)$ a diffeomorphism $u\sb0: M\to \widehat M,$ and a constant $p > n$ be given. Then sufficiently small $L\sp{p}$ bounds on the curvature of $\widehat ...