In this paper, the existence of an optimal path and its convergence to the optimal set of a primal problem of minimizing an extended real-valued function are established via a generalized augmented Lagrangian and corresponding generalized augmented Lagrangian problems, in which no convexity is imposed on the augmenting function. These results further imply a zero duality gap property between th...

We propose a new algorithm for approximate MAP inference on factor graphs, which combines augmented Lagrangian optimization with the dual decomposition method. Each slave subproblem is given a quadratic penalty, which pushes toward faster consensus than in previous subgradient approaches. Our algorithm is provably convergent, parallelizable, and suitable for fine decompositions of the graph. We...

Given a set of corrupted data drawn from a union of multiple subspace, the subspace recovery problem is to segment the data into their respective subspace and to correct the possible noise simultaneously. Recently, it is discovered that the task can be characterized, both theoretically and numerically, by solving a matrix nuclear-norm and a `2,1-mixed norm involved convex minimization problems....

Duality is an important notion for nonlinear programming (NLP). It provides a theoretical foundation for many optimization algorithms. Duality can be used to directly solve NLPs as well as to derive lower bounds of the solution quality which have wide use in other high-level search techniques such as branch and bound. However, the conventional duality theory has the fundamental limit that it le...

Abstract We show a connection between global unconstrained optimization of continuous function f and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solution v the critical Hamilton–Jacobi is built by small discount approximation as well long time limit associated evolutive equation. Then represented value control problem with target, whose optimal trajectories a...

This paper proposes a novel transmit power allocation for QAM modulated Multi-Input Multi-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) transmission. This technique consists of adapting the power allocation in the spatial domain in term of the channel conditions by the optimization process based on the optimality of the global Bit Error Rate (BER). Simulation results show sign...