Convergence of convex-concave saddle functions: applications to convex programming and mechanics

Concave and Convex Interference Functions - General Characterizations and Applications

Many resource allocation problems can be studied within the framework of interference functions. Basic properties of interference functions are non-negativity, scale-invariance, and monotonicity. In this paper, we study interference functions with additional properties, namely convexity, concavity, and log-convexity. Such interference functions occur naturally in various contexts, e.g., adaptiv...

On Convergence Rate of Concave-Convex Procedure

Concave-Convex Procedure (CCCP) has been widely used to solve nonconvex d.c.(difference of convex function) programs occur in learning problems, such as sparse support vector machine (SVM), transductive SVM, sparse principal componenent analysis (PCA), etc. Although the global convergence behavior of CCCP has been well studied, the convergence rate of CCCP is still an open problem. Most of d.c....

On the convergence of conditional epsilon-subgradient methods for convex programs and convex-concave saddle-point problems

The paper provides two contributions. First, we present new convergence results for conditional e-subgradient algorithms for general convex programs. The results obtained here extend the classical ones by Polyak [Sov. Math. Doklady 8 (1967) 593; USSR Comput. Math. Math. Phys. 9 (1969) 14; Introduction to Optimization, Optimization Software, New York, 1987] as well as the recent ones in [Math. P...

Convex and concave relaxations of implicit functions

Short Proofs of the Separation Theorems for L-convex/concave and M-convex/concave Functions

Recently K. Murota has introduced concepts of L-convex function and Mconvex function as generalizations of those of submodular function and base polyhedron, respectively, and has shown separation theorems for L-convex/concave functions and for M-convex/concave functions. The present note gives short alternative proofs of the separation theorems by relating them to the ordinary separation theore...