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We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
A natural and important generalization of submodularity -- $k$-submodularity -- applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…
We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this…
We study decentralized smooth optimization problems over compact submanifolds. Recasting it as a composite optimization problem, we propose a decentralized Douglas-Rachford splitting algorithm, DDRS. When the proximal operator of the local…
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…
This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of…
This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is a backward stochastic differential equations (BSDE). The…
We propose an algorithm for optimizing the parameters of single hidden layer neural networks. Specifically, we derive a blockwise difference-of-convex (DC) functions representation of the objective function. Based on the latter, we propose…
The difference-of-convex algorithm (DCA) is a conceptually simple method for the minimization of (possibly) nonconvex functions that are expressed as the difference of two convex functions. At each iteration, DCA constructs a global…
This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…
This paper considers convex optimization problems where nodes of a network have access to summands of a global objective. Each of these local objectives is further assumed to be an average of a finite set of functions. The motivation for…
Differential Dynamic Programming (DDP) is an efficient computational tool for solving nonlinear optimal control problems. It was originally designed as a single shooting method and thus is sensitive to the initial guess supplied. This work…
We study the problem of minimizing the sum of potentially non-differentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication in the network is not coordinated. We study the…
We consider a class of difference-of-convex (DC) optimization problems where the objective function is the sum of a smooth function and a possible nonsmooth DC function. The application of proximal DC algorithms to address this problem…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…