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Gradient-based solvers risk convergence to local optima, leading to incorrect researcher inference. Heuristic-based algorithms are able to ``break free" of these local optima to eventually converge to the true global optimum. However, given…
We study the problem of zero-order optimization of a strongly convex function. The goal is to find the minimizer of the function by a sequential exploration of its values, under measurement noise. We study the impact of higher order…
Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for…
This paper proposes a new steepest gradient descent method for solving nonconvex finite minimax problems using non-monotone adaptive step sizes and providing proof of convergence results in cases of the nonconvex, quasiconvex, and…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
We study a class of zeroth-order distributed optimization problems, where each agent can control a partial vector and observe a local cost that depends on the joint vector of all agents, and the agents can communicate with each other with…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
In this paper, we propose a novel accelerated forward-backward splitting algorithm for minimizing convex composite functions, written as the sum of a smooth function and a (possibly) nonsmooth function. When the objective function is…
We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…
Aerodynamic optimization is ubiquitous in the design of most engineering systems interacting with fluids. A common approach is to optimize a performance function defined by a choice of an aerodynamic model, e.g., turbulence RANS model, and…
This work provides the first convergence analysis for the Randomized Block Coordinate Descent method for minimizing a function that is both H\"older smooth and block H\"older smooth. Our analysis applies to objective functions that are…
First-order methods for stochastic optimization have undeniable relevance, in part due to their pivotal role in machine learning. Variance reduction for these algorithms has become an important research topic. In contrast to common…
In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…
We study the minimization of a convex function $f(X)$ over the set of $n\times n$ positive semi-definite matrices, but when the problem is recast as $\min_U g(U) := f(UU^\top)$, with $U \in \mathbb{R}^{n \times r}$ and $r \leq n$. We study…
Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same as accelerated stochastic gradient descent…
In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…
Price determination is a central research topic of revenue management in marketing. The important aspect in pricing is controlling the stochastic behavior of demand, and the previous studies have tackled price optimization problems with…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…
We study differentiable strongly quasiconvex functions for providing new properties for algorithmic and monotonicity purposes. Furthemore, we provide insights into the decreasing behaviour of strongly quasiconvex functions, applying this…