Related papers: Lagrange Duality in Set Optimization
Designing an incentive compatible auction that maximizes expected revenue is a central problem in Auction Design. While theoretical approaches to the problem have hit some limits, a recent research direction initiated by Duetting et al.…
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…
The goal of this article is to study necessary and sufficient conditions for the exactness of penalty functions and the existence of global saddle points of augmented Lagrangians for well-posed (in a suitable sense) constrained optimization…
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…
We present a parallelized primal-dual algorithm for solving constrained convex optimization problems. The algorithm is "block-based," in that vectors of primal and dual variables are partitioned into blocks, each of which is updated only by…
This paper fills a gap in the literature on natural duality theory. It concerns dual representations of categories of distributive-lattice-based algebras in which the lattice reducts are not assumed to have bounds. The development of theory…
A polynomial optimization problem (POP) consists of minimizing a multivariate real polynomial on a semi-algebraic set $K$ described by polynomial inequalities and equations. In its full generality it is a non-convex, multi-extremal,…
This paper investigates the stochastic linear-quadratic control problems with affine constraints, in which both equality and inequality constraints are involved. With the help of the Pontryagin maximum principle and Lagrangian duality…
In this work, optimality conditions and classical results from duality theory are derived for continuous-time linear optimization problems with inequality constraints. The optimality conditions are given in the Karush-Kuhn-Tucker form. Weak…
Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of…
We investigate duality and existence of dual optimizers for several adapted optimal transport problems under minimal assumptions. This includes the causal and bicausal transport, the causal and bicausal barycenter problem, and a…
In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning. Our algorithmic framework updates the primal variable…
The continuous nonlinear resource allocation problem (CONRAP) has broad applications in economics, engineering, production and inventory management, and often serves as a subproblem in complex programming. Without relying on monotonicity…
Given a convex optimization problem and its dual, there are many possible first-order algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is…
Recent results in Compressive Sensing have shown that, under certain conditions, the solution to an underdetermined system of linear equations with sparsity-based regularization can be accurately recovered by solving convex relaxations of…
Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-convex and NP-hard problem. In this paper, we investigate the dual forms…
One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the ways of addressing this difficulty is to…
The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local…
We address the problem of the existence of a Lagrangian for a given system of linear PDEs with constant coefficients. As a subtask, this involves bringing the system into a pre-Lagrangian form, wherein the number of equations matches the…
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…