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This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…

In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted…

This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…

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…

An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…

We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $\Pi$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem…

In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework,…

In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…

While optimizing convex objective (loss) functions has been a powerhouse for machine learning for at least two decades, non-convex loss functions have attracted fast growing interests recently, due to many desirable properties such as…

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…

We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…

We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence…

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…

While deep learning techniques have become extremely popular for solving a broad range of optimization problems, methods to enforce hard constraints during optimization, particularly on deep neural networks, remain underdeveloped. Inspired…

Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…

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…

We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…

In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…

We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…