Related papers: A generalized projection-based scheme for solving …
A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…
The convex feasibility problem (CFP) is at the core of the modeling of many problems in various areas of science. Subgradient projection methods are important tools for solving the CFP because they enable the use of subgradient calculations…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
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…
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…
In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
This paper shows that the optimal subgradient algorithm, OSGA, proposed in \cite{NeuO} can be used for solving structured large-scale convex constrained optimization problems. Only first-order information is required, and the optimal…
In this paper, we studied the equilibrium problem where the bi-function may be quasiconvex with respect to the second variable and the feasible set is the intersection of a finite number of convex sets. We propose a projection-algorithm,…
For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…
The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on…
Convergence of a projected stochastic gradient algorithm is demonstrated for convex objective functionals with convex constraint sets in Hilbert spaces. In the convex case, the sequence of iterates ${u_n}$ converges weakly to a point in the…
We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
When faced with multiple minima of an "inner-level" convex optimization problem, the convex bilevel optimization problem selects an optimal solution which also minimizes an auxiliary "outer-level" convex objective of interest. Bilevel…
Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…
Two new optimization techniques based on projections onto convex space (POCS) framework for solving convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost…
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…