Reformulation: Nonsmooth, Piecewise Smooth, Semismooth And Smoothing Methods (applied Optimization)
by Liqun Qi /
2010 / English / PDF
12.4 MB Download
The concept of "reformulation" has long been playing an important
role in mathematical programming. A classical example is the
penalization technique in constrained optimization that transforms
the constraints into the objective function via a penalty function
thereby reformulating a constrained problem as an equivalent or
approximately equivalent unconstrained problem. More recent trends
consist of the reformulation of various mathematical programming
prob lems, including variational inequalities and complementarity
problems, into equivalent systems of possibly nonsmooth, piecewise
smooth or semismooth nonlinear equations, or equivalent
unconstrained optimization problems that are usually
differentiable, but in general not twice differentiable. Because of
the recent advent of various tools in nonsmooth analysis, the
reformulation approach has become increasingly profound and
diversified. In view of growing interests in this active field, we
planned to organize a cluster of sessions entitled "Reformulation -
Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods" in
the 16th International Symposium on Mathematical Programming
(ismp97) held at Lausanne EPFL, Switzerland on August 24-29, 1997.
Responding to our invitation, thirty-eight people agreed to give a
talk within the cluster, which enabled us to organize thirteen
sessions in total. We think that it was one of the largest and most
exciting clusters in the symposium. Thanks to the earnest support
by the speakers and the chairpersons, the sessions attracted much
attention of the participants and were filled with great enthusiasm
of the audience.
The concept of "reformulation" has long been playing an important
role in mathematical programming. A classical example is the
penalization technique in constrained optimization that transforms
the constraints into the objective function via a penalty function
thereby reformulating a constrained problem as an equivalent or
approximately equivalent unconstrained problem. More recent trends
consist of the reformulation of various mathematical programming
prob lems, including variational inequalities and complementarity
problems, into equivalent systems of possibly nonsmooth, piecewise
smooth or semismooth nonlinear equations, or equivalent
unconstrained optimization problems that are usually
differentiable, but in general not twice differentiable. Because of
the recent advent of various tools in nonsmooth analysis, the
reformulation approach has become increasingly profound and
diversified. In view of growing interests in this active field, we
planned to organize a cluster of sessions entitled "Reformulation -
Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods" in
the 16th International Symposium on Mathematical Programming
(ismp97) held at Lausanne EPFL, Switzerland on August 24-29, 1997.
Responding to our invitation, thirty-eight people agreed to give a
talk within the cluster, which enabled us to organize thirteen
sessions in total. We think that it was one of the largest and most
exciting clusters in the symposium. Thanks to the earnest support
by the speakers and the chairpersons, the sessions attracted much
attention of the participants and were filled with great enthusiasm
of the audience.
