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We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a…
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…
Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track…
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…
Primal and dual algorithms are developed for solving the $n$-dimensional convex optimization problem of finding the Euclidean ball of minimum radius that covers $m$ given Euclidean balls, each with a given center and radius. Each algorithm…
This paper provides a set of cycling problems in linear programming. These problems should be useful for researchers to develop and test new simplex algorithms. As matter of the fact, this set of problems is used to test a recently proposed…
Consider a linear programming problem with n primal and m dual variables paired with n dual and m primal slack variables respectively, and aggregately denote these variables and slack variables as a vector z of length 2(n+m). Unlike…
This paper discusses a data-driven, empirically-based framework to make algorithmic decisions or recommendations without expert knowledge. We improve the performance of two algorithmic case studies: the selection of a pivot rule for the…
This paper investigates minimax quadratic programming problems with coupled inequality constraints. By leveraging a duality theorem, we develop a dual algorithm that extends the dual active set method to the minimax setting, transforming…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Dual first-order methods are essential techniques for large-scale constrained convex optimization. However, when recovering the primal solutions, we need $T(\epsilon^{-2})$ iterations to achieve an $\epsilon$-optimal primal solution when we…
Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…
In this work, we show that for linearly constrained optimization problems the primal-dual hybrid gradient algorithm, analyzed by Chambolle and Pock [3], can be written as an entirely primal algorithm. This allows us to prove convergence of…
Primal-dual algorithm (PDA) is a classic and popular scheme for convex-concave saddle point problems. It is universally acknowledged that the proximal terms in the subproblems about the primal and dual variables are crucial to the…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
In this paper, we study the local linear convergence properties of a versatile class of Primal-Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of…
Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…
Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias…