Optimality conditions and duality in continuous programming. I: Convex programs and a theorem of the alternative

DOI10.1016/0022-247X(80)90278-4zbMath0445.90094MaRDI QIDQ1145638

Thomas W. Reiland

Publication date: 1980

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

convex conesoptimality conditionsdualityconvex programstheorem of the alternativecontinuous programmingpolar conescontinuous time version of Farkas' theoreminfinite-dimensional programming

Mathematics Subject Classification ID

Nonlinear programming (90C30) Programming in abstract spaces (90C48) Convex sets without dimension restrictions (aspects of convex geometry) (52A05)

Related Items (23)

Approximate Solutions and Duality Theorems for Continuous-Time Linear Fractional Programming Problems ⋮ The Fritz John and Kuhn-Tucker optimality conditions in continuous-time nonlinear programming ⋮ Some remarks concerning duality for continuous-time programming problems ⋮ A constant rank constraint qualification in continuous-time nonlinear programming ⋮ Numerical method for solving the continuous-time linear programming problems with time-dependent matrices and piecewise continuous functions ⋮ Generalized concavity and duality in continuous programming ⋮ Theorems of the alternative for multifunctions with applications to optimization: General results ⋮ New optimality criteria for convex continuous-time problems of vector optimization ⋮ OPTIMALITY CONDITIONS AND DUALITY MODELS FOR A CLASS OF NONSMOOTH CONTINUOUS-TIME GENERALIZED FRACTIONAL PROGRAMMING PROBLEMS ⋮ Generalized sufficiency criteria in continuous-time programming with application to a class of variational-type inequalities ⋮ Optimality conditions and duality for a class of continuous-time generalized fractional programming problems ⋮ Using the Dinkelbach-type algorithm to solve the continuous-time linear fractional programming problems ⋮ Optimality conditions and duality in continuous programming. II: The linear problem revisited ⋮ Second-order duality for the variational problems ⋮ Using the parametric approach to solve the continuous-time linear fractional Max-min problems ⋮ Unnamed Item ⋮ KKT conditions for weak\(^\ast\) compact convex sets, theorems of the alternative, and optimality conditions ⋮ Continuous-time multiobjective fractional programming ⋮ Continuous-time generalized fractional programming ⋮ Continuous-time linear programming problems revisited: A perturbation approach ⋮ Necessary conditions for continuous-time optimization under the Mangasarian–Fromovitz constraint qualification ⋮ Optimality conditions and duality for a class of continuous-time programming problems with nonlinear operator equality and inequality constraints ⋮ Optimality conditions and Lagrangian duality in continuous-time nonlinear programming

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalized Kuhn-Tucker conditions and duality for continuous nonlinear programming problems
• Continuous time programming with nonlinear constraints
• A class of continuous linear programming problems
• A class of continuous convex programming problems
• Nonlinear programming in locally convex spaces
• An Extension of the Nonhomogeneous Farkas Theorem
• Generalizations of Farkas’ Theorem
• A Duality Theorem for a Class of Continuous Linear Programming Problems
• Duality for a Class of Infinite Programming Problems
• Generalized Kuhn–Tucker Conditions for Mathematical Programming Problems in a Banach Space
• Convergence Conditions for Nonlinear Programming Algorithms
• Symmetric Duality for Continuous Linear Programs

This page was built for publication: Optimality conditions and duality in continuous programming. I: Convex programs and a theorem of the alternative