Related papers: A Raindrop Algorithm for Searching The Global Opti…

This paper presents a practical method for finding the globally optimal solution to the sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

In this paper, we develop a global descent method for non-convex multi-objective optimization problems. The proposed approach builds upon foundational concepts from single-objective global descent techniques while removing the need for…

We present a generic coordinate descent solver for the minimization of a nonsmooth convex objective with structure. The method can deal in particular with problems with linear constraints. The implementation makes use of efficient residual…

In this work, we present a novel algorithm design methodology that finds the optimal algorithm as a function of inequalities. Specifically, we restrict convergence analyses of algorithms to use a prespecified subset of inequalities, rather…

We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…

Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…

We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…

A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…

We propose a new gradient descent algorithm with added stochastic terms for finding the global optimizers of nonconvex optimization problems. A key component in the algorithm is the adaptive tuning of the randomness based on the value of…

This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…

For solving pseudo-convex global optimization problems, we present a novel fully adaptive steepest descent method (or ASDM) without any hard-to-estimate parameters. For the step-size regulation in an $\varepsilon$-normalized direction, we…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

Optimal experimental design (OED) aims to choose the observations in an experiment to be as informative as possible, according to certain statistical criteria. In the linear case (when the observations depend linearly on the unknown…

In this paper, we develop an online optimization algorithm for solving a class of nonconvex optimization problems with a linearly varying optimal point. The global convergence of the algorithm is guaranteed using the circle criterion for…

In this paper, a sequential search method for finding the global minimum of an objective function is presented, The descent gradient search is repeated until the global minimum is obtained. The global minimum is located by a process of…

The advancement of artificial intelligence has cast a new light on the development of optimization algorithm. This paper proposes to learn a two-phase (including a minimization phase and an escaping phase) global optimization algorithm for…

Finding a local minimum or maximum of a function is often achieved through the gradient-descent optimization method. For a function in dimension d, the gradient requires to compute at each step d partial derivatives. This method is for…

We propose a general learning algorithm for solving optimization problems, based on a simple strategy of trial and adaptation. The algorithm maintains a probability distribution of possible solutions (configurations), which is updated…