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Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation…
We analyze worst-case complexity of a Proximal augmented Lagrangian (Proximal AL) framework for nonconvex optimization with nonlinear equality constraints. When an approximate first-order (second-order) optimal point is obtained in the…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
This paper proposes QPALM, a proximal augmented Lagrangian method based on quadratic approximations, for solving nonlinear programming problems with weakly convex objective and constraint functions. The algorithm is constructed by…
In the Tree Augmentation Problem (TAP) the goal is to augment a tree $T$ by a minimum size edge set $F$ from a given edge set $E$ such that $T \cup F$ is $2$-edge-connected. The best approximation ratio known for TAP is $1.5$. In the more…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
Weight optimization of frame structures with continuous cross-section parametrization is a challenging non-convex problem that has traditionally been solved by local optimization techniques. Here, we exploit its inherent semi-algebraic…
We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global…
Online learning constitutes a mathematical and compelling framework to analyze sequential decision making problems in adversarial environments. The learner repeatedly chooses an action, the environment responds with an outcome, and then the…
The Min-sum single machine scheduling problem (denoted 1||sum f_j) generalizes a large number of sequencing problems. The first constant approximation guarantees have been obtained only recently and are based on natural time-indexed LP…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
Feature selection is an important and active research area in statistics and machine learning. The Elastic Net is often used to perform selection when the features present non-negligible collinearity or practitioners wish to incorporate…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
Large-scale constrained optimization is pivotal in modern scientific, engineering, and industrial computation, often involving complex systems with numerous variables and constraints. This paper provides a unified and comprehensive…
Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…
We study quantum algorithms for approximating Lasserre's hierarchy values for polynomial optimization. Let $f,g_1,\ldots,g_m$ be real polynomials in $n$ variables and $f^\star$ the infimum of $f$ over the semialgebraic set $S(g)=\{x:…
Lagrangian methods are widely used algorithms for constrained optimization problems, but their learning dynamics exhibit oscillations and overshoot which, when applied to safe reinforcement learning, leads to constraint-violating behavior…
In this paper we study a class of constrained minimax problems. In particular, we propose a first-order augmented Lagrangian method for solving them, whose subproblems turn out to be a much simpler structured minimax problem and are…
Balkanski and Singer [5] recently initiated the study of adaptivity (or parallelism) for constrained submodular function maximization, and studied the setting of a cardinality constraint. Very recent improvements for this problem by…