The lower semi-continuous quasi-convex hull as a normalized second conjugate

DOI10.1016/0362-546X(83)90020-2zbMath0528.49007MaRDI QIDQ3310475

Ivan Singer

Publication date: 1983

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

lower semi-continuous quasi-convex hullquasi-conjugate functionalsemi-conjugate functionalsemi-dual optimizationsemi-subdifferential

Mathematics Subject Classification ID

Nonlinear programming (90C30) Weak and generalized continuity (54C08) Programming in abstract spaces (90C48) Methods involving semicontinuity and convergence; relaxation (49J45) Duality theory (optimization) (49N15) Continuity and differentiation questions (26B05) General theory of locally convex spaces (46A03) Convexity of real functions of several variables, generalizations (26B25) Abstract differentiation theory, differentiation of set functions (28A15)

Related Items

A general theory of dual optimization problems, A general theory of surrogate dual and perturbational extended surrogate dual optimization problems, Dual representations of hulls for functions satisfyingf(0) = inff(X\{0})^*, Quasiconvex duality theory by generalized conjugation methods, Conjugate functionals and level sets, Approximative quasi-subdifferentials, Set containment characterization with strict and weak quasiconvex inequalities, V -dualities and ⊥-dualities, Duality for the level sum of quasiconvex functions and applications, Quasiconjugates of functions, duality relationship between quasiconvex minimization under a reverse convex constraint and quasiconvex maximization under a convex constraint, and applications

Cites Work

• Optimization by level set methods. IV: Generalizations and complements
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