The Lagrangian Multiplier Test

A SIMPLIFIED LAGRANGIAN MULTIPLIER APPROACH FOR FIXED HEAD SHORT-TERM HYDROTHERMAL SCHEDULING

This paper presents a simplifiedlagrangian multiplier based algorithm to solve the fixed head hydrothermalscheduling problem. In fixed head hydrothermal scheduling problem, waterdischarge rate is modeled as quadratic function of hydropower generation andfuel cost is modeled as quadratic function of thermal power generation. Thepower output of each hydro unit varies with the rate of water discha...

Multiplier Algorithm Based on A New Augmented Lagrangian Function

In this paper, for nonconvex optimization problem with both equality and inequality constrains, we introduce a new augmented Lagrangian function and propose the corresponding multiplier algorithm. The global convergence is established without requiring the boundedness of multiplier sequences. In particular, if the algorithm terminates in finite steps, then we obtain a KKT point of the primal pr...

Strong Test Modules and Multiplier Ideals

We introduce the notion of strong test module and show that a large number of such modules appear in the tight closure theory of complete domains: the test ideal (this has already been known), the parameter test module, and the module of relative test elements. They also appear as certain multiplier ideals, a concept of interest in algebraic geometry.

A Multilinear Schur Test and Multiplier Operators

A multilinear version of Schur’s test is obtained for products of L spaces and is used to derive boundedness for multilinear multiplier operators acting on Sobolev and Besov spaces.

The Multiplier Ideal Is a Universal Test Ideal