We consider a decentralized stochastic optimization problem over network of agents, modeled as directed graph: Agents aim to asynchronously minimize the average their individual losses (possibly non-convex), each one having access only noisy estimate gradient its own function. propose an asynchronous distributed algorithm for such class problems. The combines gradients with tracking in push-sum...

Non-convex optimization is ubiquitous in machine learning. The MajorizationMinimization (MM) procedure systematically optimizes non-convex functions through an iterative construction and optimization of upper bounds on the objective function. The bound at each iteration is required to touch the objective function at the optimizer of the previous bound. We show that this touching constraint is u...

In this paper, we consider the optimal design of photonic crystal band structures for twodimensional square lattices. The mathematical formulation of the band gap optimization problem leads to an infinite-dimensional Hermitian eigenvalue optimization problem parametrized by the dielectric material and the wave vector. To make the problem tractable, the original eigenvalue problem is discretized...

We analyze the consensus based optimization method proposed in Pinnau et al. (2017) one dimension. rigorously provide a quantitative error estimate between point and global minimizer of given objective function. Our analysis covers general functions; we do not require any structural assumption on

Recently, Combined Heat and Power (CHP) systems have been utilized increasingly in power systems. With the addition penetration of CHP-based co-generation of electricity and heat, the determination of economic dispatch of power and heat becomes a more complex and challenging issue. The optimal operation of CHP-based systems is inherently a nonlinear and non-convex optimization problem with a lo...

To ensure efficient performance of irrigation canals, the losses from the canals need to be minimized. In this paper a modified formulation is presented to solve the optimization model for the design of different canal geometries for minimum seepage loss, in meta-heuristic environment. The complex non-linear and non-convex optimization model for canal design is solved using a probabilistic sear...

We describe two nonconventional algorithms for linear regression, called GAME and CLASH. The salient characteristics of these approaches is that they exploit the convex `1-ball and non-convex `0-sparsity constraints jointly in sparse recovery. To establish the theoretical approximation guarantees of GAME and CLASH, we cover an interesting range of topics from game theory, convex and combinatori...