Related papers: A derivative-free method for structured optimizati…
Although a large number of optimization algorithms have been proposed for black box optimization problems, the no free lunch theorems inform us that no algorithm can beat others on all types of problems. Different types of optimization…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
In this paper, a novel derivative-free pattern search based algorithm for Black-box optimization is proposed over a simplex constrained parameter space. At each iteration, starting from the current solution, new possible set of solutions…
We consider an unconstrained problem of minimizing a smooth convex function which is only available through noisy observations of its values, the noise consisting of two parts. Similar to stochastic optimization problems, the first part is…
This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…
The $\mathcal{VU}$-algorithm is a superlinearly convergent method for minimizing nonsmooth, convex functions. At each iteration, the algorithm works with a certain $\mathcal{V}$-space and its orthogonal $\U$-space, such that the…
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.…
Derivative-free algorithms seek the minimum of a given function based only on function values queried at appropriate points. Although these methods are widely used in practice, their performance is known to worsen as the problem dimension…
We propose a unified derivative-free proximal Newton-type algorithm framework for solving composite optimization problems formulated as the sum of a black-box function and a known regularization term. We establish the iteration and oracle…
Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
Saddle point optimization is a critical problem employed in numerous real-world applications, including portfolio optimization, generative adversarial networks, and robotics. It has been extensively studied in cases where the objective…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
A new universal derivative-free optimization method CDOS (Conjugate Direction with Orthogonal Shift) is proposed. The CDOS method was specially developed to solve optimization tasks where the objective function and constraints are black…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
For safety-critical black-box optimization tasks, observations of the constraints and the objective are often noisy and available only for the feasible points. We propose an approach based on log barriers to find a local solution of a…
This paper describes a simple, but effective sampling method for optimizing and learning a discrete approximation (or surrogate) of a multi-dimensional function along a one-dimensional line segment of interest. The method does not rely on…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…