<p>In this article, we propose a steepest descent method for unconstrained <i>multiobjective interval optimization problems</i> (MIOPs). After establishing a relationship between weakly Pareto optimal points and Pareto critical points of an MIOP, we develop an algorithm to find a Pareto critical point of the MIOP. In this algorithm, we provide the computation of a descent direction at a non-Pareto critical point for an MIOP. Further, we use Armijo-like rule to find the step length. We prove the existence of the step length and derive an estimation of its lower bound. Under certain assumptions, we prove that the sequence generated by the proposed algorithm converges to the Pareto critical point of the MIOP. In addition, we show that our proposed algorithm has a rate of convergence of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11075_2025_2205_Article_IEq1.gif" Format="GIF" Height="33" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{O}\left( \tfrac{\varvec{1}}{\varvec{\sqrt{k}}}\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mi mathvariant="bold-italic">O</mi> </mrow> <mfenced close=")" open="("> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mn mathvariant="bold">1</mn> </mrow> <mrow> <msqrt> <mi mathvariant="bold-italic">k</mi> </msqrt> </mrow> </mfrac> </mstyle> </mfenced> </mrow> </math></EquationSource> </InlineEquation> for nonconvex, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11075_2025_2205_Article_IEq2.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{O}\left( \tfrac{\varvec{1}}{\varvec{k}}\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mi mathvariant="bold-italic">O</mi> </mrow> <mfenced close=")" open="("> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mn mathvariant="bold">1</mn> </mrow> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> </mfrac> </mstyle> </mfenced> </mrow> </math></EquationSource> </InlineEquation> for convex, and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11075_2025_2205_Article_IEq3.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{O}\left( \varvec{\gamma }^{\varvec{k}}\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mi mathvariant="bold-italic">O</mi> </mrow> <mfenced close=")" open="("> <msup> <mrow> <mi mathvariant="bold-italic">γ</mi> </mrow> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> </msup> </mfenced> </mrow> </math></EquationSource> </InlineEquation> with some <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11075_2025_2205_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{\gamma }\varvec{\in } \varvec{(0,1)}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mi mathvariant="bold-italic">γ</mi> </mrow> <mrow> <mo mathvariant="bold">∈</mo> </mrow> <mrow> <mo mathvariant="bold" stretchy="false">(</mo> <mn mathvariant="bold">0</mn> <mo mathvariant="bold">,</mo> <mn mathvariant="bold">1</mn> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for strongly convex multiobjective interval-valued mappings. Finally, we provide numerical validation and performance of our proposed algorithm through some test problems.</p>