In this article, we propose a dual set membership filter for nonlinear dynamic systems with additive unknown but bounded noises, and it has three distinct advantages. First, the system is translated into linear by leveraging semi-infinite programming, rather than linearizing function. The programming to find an ellipsoid bounding transformation of ellipsoid, which aims compute tight cover state...

This paper deals with the Frank–Wolfe algorithm to solve a special class of non-compact constrained optimization problems. The notion asymptotic cone is one main concept used introduce problems considered as well establish definition algorithm. problems, closed and convex constraint set, are characterized by two conditions on gradient objective function. first establishes that function Lipschit...

We present a survey of recent work on the problem of learning a distance metric in the framework of semidefinite programming (SDP). Along with a brief theoretical background on convex optimization and distance metrics, we present various methods developed in this context under different approaches and provide theoretical analysis for a subset of them. A gradient ascent projection algorithm (Xin...

In this work, we consider a class of nonlinear optimization problems with convex constraints with the aim of computing sparse solutions. This is an important task arising in various fields such as machine learning, signal processing, data analysis. We adopt a concave optimization-based approach, we define an effective version of the Frank-Wolfe algorithm, and we prove the global convergence of ...

Finding a feasible solution to aMIP problem is a tough task that has receivedmuch attention in the last decades. The Feasibility Pump (FP) is a heuristic for finding feasible solutions to MIP problems that has encountered a lot of success as it is very efficient also when dealing with very difficult instances. In this work, we show that the FP heuristic for general MIP problems can be seen as t...

In this work we introduce a conditional accelerated lazy stochastic gradient descent algorithm with optimal number of calls to a stochastic first-order oracle and convergence rate O( 1 ε2 ) improving over the projection-free, Online Frank-Wolfe based stochastic gradient descent of Hazan and Kale [2012] with convergence rate O( 1 ε4 ).

Conditional gradient algorithms (also often called Frank-Wolfe algorithms) are popular due to their simplicity of only requiring a linear optimization oracle and more recently they also gained significant traction for online learning. While simple in principle, in many cases the actual implementation of the linear optimization oracle is costly. We show a general method to lazify various conditi...

In the preceding paper, we demonstrated the existence of the dynamic system of the traffic assignment problem (TAP), called J-system, whose steady states are J-equilibria (JE) and only stable steady states are user-equilibria (UE). Based on this new definition of UE, in this paper, we develop algorithms for computing both JE and UE of general transportation networks. To find JE, we can use Newt...

Abstract The computational bottleneck in distributed optimization methods, which is based on projected gradient descent, due to the computation of a full vector and projection step. This particular problem for large datasets. To reduce complexity existing we combine randomized block-coordinate descent Frank–Wolfe techniques, then propose projection-free algorithm over networks, where each agent...