The accelerated proximal gradient (APG) method, first proposed by Nesterov for minimizing smooth convex functions, later extended by Beck and Teboulle to composite convex objective functions, and studied in a unifying manner by Tseng, has proven to be highly efficient in solving some classes of large scale structured convex optimization (possibly nonsmooth) problems, including nuclear norm mini...

The relaxation in the calculus of variation motivates numerical analysis a class degenerate convex minimization problems with non-strictly energy densities some convexity control and two-sided $p$-growth. minimizers may be non-unique primal variable but lead to unique stress $\sigma \in H(\operatorname{div},\Omega;\mathbb{M})$. Examples include p-Laplacian, an optimal design problem topology op...

Conjugate gradient methods are efficient for smooth optimization problems, while there are rare conjugate gradient based methods for solving a possibly nondifferentiable convex minimization problem. In this paper by making full use of inherent properties of Moreau-Yosida regularization and descent property of modified conjugate gradient method we propose a modified Fletcher-Reeves-type method f...

A compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. Directed Hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. Sets of extrema of Birkhoff polyhedra are mapped to tours ...

We d e r i v e t h e L i p s c h i t z dependence of t h e s e t of s o l u t i o n s of a convex minimizat ion problem and i t s Lagrange m u l t i p l i e r s upon t h e n a t u r a l parameters from an Inve r se Funct ion Theorem f o r se t -valued maps. Th i s r e q u i r e s t h e use of con t ingen t and Clarke d e r i v a t i v e s of se t -valued maps, a s w e l l a s gene ra l i zed se...

We present a variational reformulation of a class of doubly nonlinear parabolic equations as (limits of) constrained convex minimization problems. In particular, an ε−dependent family of weighted energy-dissipation (WED) functionals on entire trajectories is introduced and proved to admit minimizers. These minimizers converge to solutions of the original doubly nonlinear equation as ε → 0. The ...