Related papers: Differentiating through Log-Log Convex Programs
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
Logarithms of determinants of large positive definite matrices appear ubiquitously in machine learning applications including Gaussian graphical and Gaussian process models, partition functions of discrete graphical models, minimum-volume…
We introduce the online stochastic Convex Programming (CP) problem, a very general version of stochastic online problems which allows arbitrary concave objectives and convex feasibility constraints. Many well-studied problems like online…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
An emerging class of trajectory optimization methods enforces collision avoidance by jointly optimizing the robot's configuration and a separating hyperplane. However, as linear separators only apply to convex sets, these methods require…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
The $\epsilon$-subdifferential of convex univariate piecewise linear-quadratic functions can be computed in linear worst-case time complexity as the level-set of a convex function. Using dichotomic search, we show how the computation can be…
Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…
In this work, we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints. The solution is given in closed-form as a function of some Lagrange multipliers that can be computed through…
We propose FlexQP, an always-feasible convex quadratic programming (QP) solver based on an $\ell_1$ elastic relaxation of the QP constraints. If the original constraints are feasible, FlexQP provably recovers the optimal solution. If the…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
This paper aims to find efficient solutions to a multi-objective optimization problem (MP) with convex polynomial data. To this end, a hybrid method, which allows us to transform problem (MP) into a scalar convex polynomial optimization…
Convex variational problems arise in many fields ranging from image processing to fluid and solid mechanics communities. Interesting applications usually involve non-smooth terms which require well-designed optimization algorithms for their…
Non-convex optimization problems are pervasive across mathematical programming, engineering design, and scientific computing, often posing intractable challenges for traditional solvers due to their complex objective functions and…
CVXR is an R package that provides an object-oriented modeling language for convex optimization, similar to CVX, CVXPY, YALMIP, and Convex.jl. It allows the user to formulate convex optimization problems in a natural mathematical syntax…
Coded distributed computation has become common practice for performing gradient descent on large datasets to mitigate stragglers and other faults. This paper proposes a novel algorithm that encodes the partial derivatives themselves and…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…