Related papers: Optimizing Low Dimensional Functions over the Inte…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
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…
Interior point methods for solving linearly constrained convex programming involve a variable projection matrix at each iteration to deal with the linear constraints. This matrix often becomes ill-conditioned near the boundary of the…
We derive lower bounds on the black-box oracle complexity of large-scale smooth convex minimization problems, with emphasis on minimizing smooth (with Holder continuous, with a given exponent and constant, gradient) convex functions over…
Functionally constrained stochastic optimization problems, where neither the objective function nor the constraint functions are analytically available, arise frequently in machine learning applications. In this work, assuming we only have…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…
While recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a…
We address optimization of nonlinear functions of the form $f(Wx)$, where $f:\R^d\to \R$ is a nonlinear function, $W$ is a $d\times n$ matrix, and feasible $x$ are in some large finite set $F$ of integer points in $\R^n$. One motivation is…
In bi-objective integer optimization the optimal result corresponds to a set of non-dominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available…
We consider the problem of chasing convex functions, where functions arrive over time. The player takes actions after seeing the function, and the goal is to achieve a small function cost for these actions, as well as a small cost for…
In this paper, we present the first outer approximation algorithm for multi-objective mixed-integer linear programming problems with any number of objectives. The algorithm also works for certain classes of non-linear programming problems.…
In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective…
One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and…
We consider the problem of minimizing a smooth, Lipschitz, convex function over a compact, convex set using sub-zeroth-order oracles: an oracle that outputs the sign of the directional derivative for a given point and a given direction, an…
We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an…
We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \in [0,1]^{m \times n}$, a vector $b \in [1,\infty)^m$, and a monotone…
In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…
The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional…