Convex optimization information

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...

real number). Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where...

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

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...

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

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

functions and convex sets, often with applications in convex minimization, a subdomain of optimization theory. A subset C ⊆ X {\displaystyle C\subseteq X}...

Conditions in Convex Optimization: A Finite-Dimensional View. CRC Press. p. 243. ISBN 9781439868225. Neustadt, Lucien W. (2015-03-08). Optimization: A Theory...

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

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

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...

to solve non-differentiable convex optimization problems. Many interesting problems can be formulated as convex optimization problems of the form min x...

monomials. Geometric programming is closely related to convex optimization: any GP can be made convex by means of a change of variables. GPs have numerous...

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

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...

In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function...

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

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

In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions over convex sets. The ellipsoid method generates...

science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided...

formulated as problems on convex sets or convex bodies. Six kinds of problems are particularly important:: Sec.2  optimization, violation, validity, separation...

(2016), Tuy, Hoang (ed.), "Polynomial Optimization", Convex Analysis and Global Optimization, Springer Optimization and Its Applications, vol. 110, Cham:...

mathematical analysis, in mathematical optimization, and in game theory and economics. In nonlinear optimization, quasiconvex programming studies iterative...