Related papers: Mirror-Descent Methods in Mixed-Integer Convex Opt…
Consider an oracle which takes a point $x$ and returns the minimizer of a convex function $f$ in an $\ell_2$ ball of radius $r$ around $x$. It is straightforward to show that roughly $r^{-1}\log\frac{1}{\epsilon}$ calls to the oracle…
In this work, we consider a distributed online convex optimization problem, with time-varying (potentially adversarial) constraints. A set of nodes, jointly aim to minimize a global objective function, which is the sum of local convex…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected,…
We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Holder-smooth…
This paper studies first order methods for solving smooth minimax optimization problems $\min_x \max_y g(x,y)$ where $g(\cdot,\cdot)$ is smooth and $g(x,\cdot)$ is concave for each $x$. In terms of $g(\cdot,y)$, we consider two settings --…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
We study a class of convex-concave saddle-point problems of the form $\min_x\max_y \langle Kx,y\rangle+f_{\cal{P}}(x)-h^\ast(y)$ where $K$ is a linear operator, $f_{\cal{P}}$ is the sum of a convex function $f$ with a Lipschitz-continuous…
Recently classes of conic and discrete conic functions were introduced. In this paper we use the term convic instead conic. The class of convic functions properly includes the classes of convex functions, strictly quasiconvex functions and…
In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…
We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…
In this paper we consider the problem of minimizing a general quadratic function over the mixed integer points in an ellipsoid. This problem is strongly NP-hard, NP-hard to approximate within a constant factor, and optimal solutions can be…
The study of convex functions - in particular, of their optimization (really minimization) is one of the most important fields of applied mathematics. Convexity seems to be one of those incredibly well-chosen hypotheses which is just…
This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…
We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…
Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…
A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on…