Related papers: Mirror-Descent Methods in Mixed-Integer Convex Opt…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…
Given a posimodular function $f: 2^V \to \mathbb{R}$ on a finite set $V$, we consider the problem of finding a nonempty subset $X$ of $V$ that minimizes $f(X)$. Posimodular functions often arise in combinatorial optimization such as…
We study the complexity of optimizing highly smooth convex functions. For a positive integer $p$, we want to find an $\epsilon$-approximate minimum of a convex function $f$, given oracle access to the function and its first $p$ derivatives,…
Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by…
We address the problem of minimizing a convex smooth function $f(x)$ over a compact polyhedral set $D$ given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as…
We consider the problem of minimizing a convex objective function $F$ when one can only evaluate its noisy approximation $\hat{F}$. Unless one assumes some structure on the noise, $\hat{F}$ may be an arbitrary nonconvex function, making the…
The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of…
We tackle the Optimal Experiment Design Problem, which consists of choosing experiments to run or observations to select from a finite set to estimate the parameters of a system. The objective is to maximize some measure of information…
Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and…
Maximizing a DR-submodular function subject to a general convex set is an NP-hard problem arising from many applications in combinatorial optimization and machine learning. While it is highly desirable to design efficient approximation…
This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number…
We consider the problem of minimizing a composite convex function with two different access methods: an oracle, for which we can evaluate the value and gradient, and a structured function, which we access only by solving a convex…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
Given real numbers whose sum is an integer, we study the problem of finding integers which match these real numbers as closely as possible, in the sense of L^p norm, while preserving the sum. We describe the structure of solutions for this…
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…
In this paper, the optimal convergence rate $O\left(N^{-1/2}\right)$ (where $N$ is the total number of iterations performed by the algorithm), without the presence of a logarithmic factor, is proved for mirror descent algorithms with…
DR-submodular functions encompass a broad class of functions which are generally non-convex and non-concave. We study the problem of minimizing any DR-submodular function, with continuous and general integer variables, under box constraints…
This letter presents an almost sure convergence of the zeroth-order mirror descent algorithm. The algorithm admits non-smooth convex functions and a biased oracle which only provides noisy function value at any desired point. We approximate…