Area minimizing sets subject to a volume constraint in a convex set

N ov 1 99 8 Area Minimizing Sets Subject to a Volume Constraint in a Convex Set

An efficient method for minimizing a convex separable logarithmic function subject to a convex inequality constraint or linear equality constraint

We consider the problem of minimizing a convex separable logarithmic function over a region defined by a convex inequality constraint or linear equality constraint, and twosided bounds on the variables (box constraints). Such problems are interesting from both theoretical and practical point of view because they arise in somemathematical programming problems as well as in various practical prob...

Minimizing a Convex Cost Closure Set

Many applications in the area of production and statistical estimation are problems of convex optimization subject to ranking constraints that represent a given partial order. This problem – which we call the convex cost closure problem, or (CCC) – is a generalization of the known maximum (or minimum) closure problem and the isotonic regression problem. For a (CCC) problem on n variables and m ...

A Semidefinite Optimization Approach to Quadratic Fractional Optimization with a Strictly Convex Quadratic Constraint

In this paper we consider a fractional optimization problem that minimizes the ratio of two quadratic functions subject to a strictly convex quadratic constraint. First using the extension of Charnes-Cooper transformation, an equivalent homogenized quadratic reformulation of the problem is given. Then we show that under certain assumptions, it can be solved to global optimality using semidefini...

Using a Natural Constraint to Approximate Area and Volume

This paper presents methods to calculate the 2D area (or the 3D volume) enclosed by a plane curve (or space surface) without analytical expression. One property of our methods is that the error of the measurement is proportional to the square of the measuring unit when the unit is small enough. Finally, w e p o i n t out a property common to calculating area and volume using the corresponding a...