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In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
Information compression is essential to reduce communication cost in distributed optimization over peer-to-peer networks. This paper proposes a communication-efficient linearly convergent distributed (COLD) algorithm to solve strongly…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
We introduce and study various algorithms for solving nonconvex minimization with inequality constraints, based on the construction of convex surrogate envelopes that majorize the objective and the constraints. In the case where the…
We propose a new framework for deriving screening rules for convex optimization problems. Our approach covers a large class of constrained and penalized optimization formulations, and works in two steps. First, given any approximate point,…
The convex restriction of the power flow feasible sets identifies the convex subset of power injections where the solution for power flow is guaranteed to exist and satisfy the operational constraints. In contrast to convex relaxations, the…
We describe a convex programming approach to the calculation of lower bounds on the minimum cost of constrained decentralized control problems with nonclassical information structures. The class of problems we consider entail the…
Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
In this paper we study a nonconvex-strongly-concave constrained minimax problem. Specifically, we propose a first-order augmented Lagrangian method for solving it, whose subproblems are nonconvex-strongly-concave unconstrained minimax…
In this note, three Lagrange multiplier rules introduced in the literature for set valued optimization problems are compared. A generalization of all three results is given which proves that under rather mild assumptions, $x$ is a weak…
In this paper, the elliptic PDE-constrained optimization problem with box constraints on the control is studied. To numerically solve the problem, we apply the 'optimize-discretize-optimize' strategy. Specifically, the alternating direction…
Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by…
We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…
In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…
This paper proposes tight semidefinite relaxations for polynomial optimization. The optimality conditions are investigated. We show that generally Lagrange multipliers can be expressed as polynomial functions in decision variables over the…