Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently...

generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from...

In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives...

Lectures on Convex Optimization: A Basic Course. Kluwer Academic Publishers. pp. 63–64. ISBN 9781402075537. Nemirovsky and Ben-Tal (2023). "Optimization III:...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions....

methods for convex optimization: a survey. Optimization for Machine Learning, 85. Hazan, Elad (2015). Introduction to Online Convex Optimization (PDF). Foundations...

linear to convex optimization problems, based on a self-concordant barrier function used to encode the convex set. Any convex optimization problem can...

have the property of being closed and convex. They are important concepts in the fields of convex optimization, variational inequalities and projected...

Demand optimization Destination dispatch — an optimization technique for dispatching elevators Energy minimization Entropy maximization Highly optimized tolerance...

Method for Convex Optimization". SIAM Review. 65 (2): 539–562. doi:10.1137/21M1390037. ISSN 0036-1445. Kim, D.; Fessler, J. A. (2016). "Optimized First-order...

In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective...

an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem...

Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the...

internationally recognized expert in convex optimization, especially in the development of efficient algorithms and numerical optimization analysis. He is currently...

single-objective optimization cases are presented. In the second part, test functions with their respective Pareto fronts for multi-objective optimization problems...

In mathematical optimization, a quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and...

necessarily convex) compact set defined by inequalities g i ( x ) ⩾ 0 , i = 1 , … , r {\displaystyle g_{i}(x)\geqslant 0,i=1,\ldots ,r} . Global optimization is...

function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets. The...

learning rates. While designed for convex problems, AdaGrad has been successfully applied to non-convex optimization. RMSProp (for Root Mean Square Propagation)...

Robust optimization is a field of mathematical optimization theory that deals with optimization problems in which a certain measure of robustness is sought...

Bayesian optimization is a sequential design strategy for global optimization of black-box functions, that does not assume any functional forms. It is...

Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization, some or all of the...

Subgradient methods are convex optimization methods which use subderivatives. Originally developed by Naum Z. Shor and others in the 1960s and 1970s,...

Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute...

optimization algorithm for constrained convex optimization. Also known as the conditional gradient method, reduced gradient algorithm and the convex combination...

programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject...

Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine...

of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate...

A second-order cone program (SOCP) is a convex optimization problem of the form minimize   f T x   {\displaystyle \ f^{T}x\ } subject to ‖ A i x + b i...