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Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…

This paper presents a new column-and-constraint generation method for two-stage robust mixed-integer programs with finite uncertainty sets. Our method combines and extends speed-up techniques used in previous column-and-constraint…

An inverse problem of identifying inhomogeneity or crack in the workpiece made of nonlinear magnetic material is investigated. To recover the shape from the local measurements, a piecewise constant level set algorithm is proposed. By means…

Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…

In this paper, we propose an optimally structured gradient coding scheme to mitigate the straggler problem in distributed learning. Conventional gradient coding methods often assume homogeneous straggler models or rely on excessive data…

In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear…

We consider the convex minimization model with both linear equality and inequality constraints, and reshape the classic augmented Lagrangian method (ALM) by balancing its subproblems. As a result, one of its subproblems decouples the…

This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating conic program for separating disjunctive cuts, and investigate the impact of the normalization…

We investigate a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…

The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…

A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…

In this paper we examine how Lagrangian techniques can be used to compute underapproximations and overapproximation of the finite-time horizon, stochastic reach-avoid level sets for discrete-time, nonlinear systems. This approach is…

Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…

In this paper, we consider numerical approximations for the optimal partition problem using Lagrange multipliers. By rewriting it into constrained gradient flows, three and four steps numerical schemes based on the Lagrange multiplier…

This paper is concerned with augmented Lagrangian methods for the treatment of fully convex composite optimization problems. We extend the classical relationship between augmented Lagrangian methods and the proximal point algorithm to the…

We consider a multi-agent optimization problem where agents subject to local, intermittent interactions aim to minimize a sum of local objective functions subject to a global inequality constraint and a global state constraint set. In…

Sparse ridge regression is widely utilized in modern data analysis and machine learning. However, computing globally optimal solutions for sparse ridge regression is challenging, particularly when samples are arbitrarily given or generated…

We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…

We address combinatorial optimization problems with uncertain coefficients varying over ellipsoidal uncertainty sets. The robust counterpart of such a problem can be rewritten as a second-oder cone program (SOCP) with integrality…

Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…