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This paper studies distributed algorithms for the extended monotropic optimization problem, which is a general convex optimization problem with a certain separable structure. The considered objective function is the sum of local convex…
The objective of this study is to present a novel, efficient, and fast direct method for solving linear systems of equations whose coefficient matrix is a tridiagonal Quasi-Toeplitz matrix. Such matrices are frequently encountered in the…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
In this paper, we study possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear semidefinite programming problems and more general nonlinear and nonsmooth cone constrained optimization…
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…
Optimization on Hadamard manifolds -- the natural Riemannian setting for globally geodesically convex problems -- relies on exponential maps to retract tangent vectors and parallel transport to connect tangent spaces across the manifold.…
This paper addresses the challenge of accommodating nonlinear dynamics and constraints in rapid trajectory optimization, envisioned for use in the context of onboard guidance. We present a novel framework that uniquely employs…
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…
The maximum function, on vectors of real numbers, is not differentiable. Consequently, several differentiable approximations of this function are popular substitutes. We survey three smooth functions which approximate the maximum function…
A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…
We consider discrete linear Chebyshev approximation problems in which the unknown parameters of linear function are fitted by minimizing the maximum absolute deviation of errors. Such problems find application in the solution of…
Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best solution in this set is in general a challenging task: In the case of three or more objectives…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
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…
We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
Non-convex optimal control problems occurring in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and…
We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…
In this paper we consider constrained optimization problems where both the objective and constraint functions are of the black-box type. Furthermore, we assume that the nonlinear inequality constraints are non-relaxable, i.e. their values…