Machine learning is most often cast as an optimization problem. Ideally, one expects a convex objective function to rely on efficient convex optimizers with nice guarantees such as no local optima. Yet, non-convexity is very frequent in practice and it may sometimes be inappropriate to look for convexity at any price. Alternatively one can decide not to limit a priori the modeling expressivity ...

In the conic formulation of a convex optimization problem the constraints are expressed as linear inequalities with respect to a possibly non-polyhedral convex cone. This makes it possible to formulate elegant extensions of interior-point methods for linear programming to general nonlinear convex optimization. Recent research on cone programming algorithms has particularly focused on three conv...

A generic algorithm is developed to reduce the problem of obtaining linear and nonlinear entanglement witnesses of a given quantum system, to convex optimization problem. This approach is completely general and can be applied for the entanglement detection of any N-partite quantum system. For this purpose, a map from convex space of separable density matrices to a convex region called feasible ...

This paper is a follow up to the previous author’s paper on convex optimization. In that paper we began the process of adjusting greedytype algorithms from nonlinear approximation for finding sparse solutions of convex optimization problems. We modified there three the most popular in nonlinear approximation in Banach spaces greedy algorithms – Weak Chebyshev Greedy Algorithm, Weak Greedy Algor...

In this article, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that is concept naturally suitable state estimation, existing solutions are either local or relatively conservative when applying physical systems. To address this, show problem can be translated into an...

The growing costs of fuel and operation of power generating units warrant improvement of optimization methodologies for economic dispatch (ED) problems. The practical ED problems have non-convex objective functions with equality and inequality constraints that make it much harder to find the global optimum using any mathematical algorithms. Modern optimization algorithms are often meta-heuristi...

Nonlinear systems with time-varying uncertainties with known norm bound and exogenous disturbances are investigated in this work. Conditions for the determination of the H∞ norm of this class of systems are obtained in the form of a convex optimization problem in terms of LMIs. It is also proposed a H∞ optimal control design that aims to stabilize a class of nonlinear systems with time-varying ...

L-convex functions are nonlinear discrete functions on integer points that are computationally tractable in optimization. In this paper, a discrete Hessian matrix and a local quadratic expansion are defined for L-convex functions. We characterize L-convex functions in terms of the discrete Hessian matrix and the local quadratic expansion.